Copyright 2015 Edmentum All rights reserved.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Copyright 2015 Edmentum All rights reserved."

Transcription

1 Triangles 1. A triangle has 2 angles that each measure 71. A. isosceles triangle B. right triangle C. obtuse triangle D. equiangular triangle Copyright 2015 Edmentum All rights reserved. 2. Directions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number. There are different triangles he can create that fit these conditions. Of these triangles, there are isosceles, scalene, and equilateral. 3. Which of the following are acute scalene triangles? W. X. Y. Z. A. X and Y only B. Y and Z only C. W, X, and Y only D. X, Y, and Z only 4. A triangle has one angle that measures 68 degrees, one angle that measures 46 degrees, and one angle that measures 66 degrees. A. obtuse triangle B. equilateral triangle practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

2 C. right triangle D. acute triangle 5. How many triangles exist with the given side lengths? A. No triangle exists with the given side lengths. 12 in, 15 in, 18 in B. More than one triangle exists with the given side lengths. C. Exactly one unique triangle exists with the given side lengths. 6. *triangle not drawn to scale 6 units 5 units 9 units What kind of triangle is this? A. scalene triangle B. equilateral triangle C. right triangle D. isosceles triangle 12 units 7. *triangle not drawn to scale 12 units 20 units What kind of triangle is this? A. equilateral triangle B. obtuse triangle C. isosceles triangle D. right triangle 16 units 8. A bridge contains beams that form triangles, as shown below. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

3 Which of the following best describes the triangle with the given measures? A. acute isosceles triangle B. obtuse isosceles triangle C. obtuse scalene triangle D. acute scalene triangle 9. A triangle has 2 angles that measure 60. A. right triangle B. scalene triangle C. obtuse triangle D. equiangular triangle 10. In triangle ABC, the length of side AB is 18 inches and the length of side BC is 23 inches. Which of the following could be the length of side AC? A. 43 inches B. 3 inches C. 46 inches D. 35 inches 11. A triangle has 3 sides that each equal 13 cm. A. obtuse triangle B. right triangle C. equilateral triangle D. scalene triangle 12. A triangle has one angle that measures 27 degrees, one angle that measures 135 degrees, and one angle that measures 18 degrees. A. obtuse triangle B. equilateral triangle C. acute triangle D. right triangle 13. How many triangles exist with the given angle measures? 30, 65, 85 A. More than one triangle exists with the given angle measures. B. No triangle exists with the given angle measures. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

4 C. Exactly one unique triangle exists with the given angle measures. 14. Directions: Select the correct answer from each drop down menu. Shelbie has been asked to construct as many unique triangles as she can that have all sides of integer length, one side of length 5 cm, and a perimeter less than or equal to 16 cm. Shelbie can construct unique triangles of which are strictly isosceles and equilateral. 15. Which of the following is false? A. A triangle can be drawn with exactly one obtuse angle. B. A triangle can be drawn with more than one acute angle. C. A triangle can be drawn with exactly one right angle. D. A triangle can be drawn with exactly one acute angle. 16. Meena has a pair of blue jeans with the design below on its back pockets. Which of the following best describes the triangle with the given measures? A. acute equilateral triangle B. acute isosceles triangle C. obtuse equilateral triangle D. obtuse isosceles triangle 17. How many triangles exist with the given side lengths? A. No triangle exists with the given side lengths. 4 m, 4 m, 7 m B. More than one triangle exists with the given side lengths. C. Exactly one unique triangle exists with the given side lengths. 18. In triangle ABC, the length of side AB is 20 inches and the length of side BC is 29 inches. Which of the following could be the length of side AC? practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

5 A. 44 inches B. 51 inches C. 54 inches D. 7 inches 19. How many triangles exist with the given angle measures? 80, 50, 50 A. No triangle exists with the given angle measures. B. Exactly one unique triangle exists with the given angle measures. C. More than one triangle exists with the given angle measures. 20. How many triangles exist with the given angle measures? 55, 45, 90 A. No triangle exists with the given angle measures. B. Exactly one unique triangle exists with the given angle measures. C. More than one triangle exists with the given angle measures. Answers 1. A A 4. D 5. C 6. A 7. D 8. C 9. D 10. D 11. C 12. A 13. A D 16. A 17. C 18. A 19. C 20. A Explanations 1. Since in any given triangle, the interior angles add together to equal 180, subtract the measure of each of the first 2 angles from 180 to find the measure of the third angle. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

6 = 38 So, this triangle is not equiangular, but has only 2 angles of equal measure. A triangle that has at least 2 equal angles is called an isosceles triangle. 2. First, sketch all the possible triangles Theo can make using pieces of wood that are each five feet long. In order for the perimeter of the triangle to be a whole number, the side of the triangle that is against his house must also be a whole number. No other triangles can be made because the two pieces of wood cannot be spread out anymore and still leave a whole number value for the triangle side that is against his house. So, there are 9 possible triangles he can create that fit the conditions. Look at the sketches. For a triangle to be isosceles, at least two sides must be the same length. Since at least two sides have the same length in every triangle, 9 of the triangles are isosceles. For a triangle to be scalene, none of the sides can have the same length. Since there is no triangle where none of the sides have the same length, 0 of the triangles are scalene. For a triangle to be equilateral, all of the sides must have the same length. Since there is only one triangle where all the sides are the same length, 1 of the triangles is equilateral. 3. Triangle W is a right scalene triangle. Triangle X is an acute scalene triangle. Triangle Y is an acute scalene triangle. Triangle Z is an obtuse scalene triangle. Therefore, X and Y only are acute scalene triangles. 4. An acute triangle is a triangle with all the angles less than According to the triangle inequality theorem, the sum of any two sides must be greater than the third side. Since the sum of 12 in and 15 in is greater than 18 in, the side lengths do form a triangle. A triangle with no congruent sides is a scalene triangle. Only one scalene triangle with side lengths of 12 in, 15 in, and 18 in exists. Therefore, exactly one unique triangle exists with the given side lengths. 6. A scalene triangle is a triangle with NO congruent sides and NO congruent angles. 7. A triangle that contains a right angle is called a right triangle. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

7 7. A triangle that contains a right angle is called a right triangle. 8. The triangle has an angle with a measure greater than 90, so the triangle is an obtuse triangle. The triangle does not have any congruent sides, so the triangle is a scalene triangle. Therefore, the triangle is best described as an obtuse scalene triangle. 9. Since in any given triangle, the interior angles add together to equal 180, subtract the measure of each of the first 2 angles from 180 to find the measure of the third angle = 60 So, this triangle has 3 equal angles. A triangle that has 3 equal angles is called an equiangular triangle. 10. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the third side. Since the two given sides have lengths of 18 inches and 23 inches, the third side, AC, must fit the following inequalities. AC < 18 inches + 23 inches = 41 inches and AC > 23 inches 18 inches = 5 inches Thus, 5 inches < AC < 41 inches. Of the answer choices given, 35 inches is the only choice that falls within this range. 11. An equilateral triangle has 3 equal sides. All the angles in an equilateral triangle are equal as well. 12. An obtuse triangle is a triangle that has one angle that is greater than The sum of the angles in a triangle is 180, so the angles do form a triangle. Since all three angles are different, the triangle is a scalene triangle. An infinite number of scalene triangles exist with different side lengths. Therefore, more than one triangle exists with the given angle measures. 14. Based on the restrictions of all sides of integer length, one side of length 5 cm, and a perimeter less than or equal to 16 cm, start by making a list. Keep in mind that that two shorter sides of a triangle must add together to be greater than the third side. Start by looking at the cases in which 5 cm is one of the short sides. If the two short sides are 1 cm and 5 cm, then the remaining side has to be less than 6 cm, which only leaves 5 cm as an option. Since = 10, a triangle with sides of 1 cm, 5 cm, 5 cm is within the perimeter limitations. If the two short sides are 2 cm and 5 cm, then the remaining side has to be less than 7 cm, which leaves 5 cm and 6 cm as options. Since = 9, both of these options are viable. Triangles with sides of 2 cm, 5 cm, 5 cm, and 2 cm, 5 cm, 6 cm are within the perimeter limitations. If the two short sides are 3 cm and 5 cm, then the remaining side has to be less than 8 cm, which leaves 5 cm, 6 cm, and 7 cm as options. Since = 8, all of these options are viable. Triangles with sides of 3 cm, 5 cm, 5 cm; 3 cm, 5 cm, 6 cm; and 3 cm, 5 cm, 7 cm are within the perimeter limitations. If the two short sides are 4 cm and 5 cm, then the remaining side has to be less than 9 cm, which leaves 5 cm, 6 cm, 7 cm, and 8 cm as options. Since = 7, only the triangles with sides of 4 cm, 5 cm, 5 cm; 4 cm, 5 cm, 6 cm; and 4 cm, 5 cm, 7 cm are within the perimeter limitations. If the two short sides are 5 cm and 5 cm, then the remaining side has to be less than 10 cm, which leaves 5 cm, 6 cm, 7 cm, 8 cm, and 9 cm as options. Since = 6, only the triangles with sides of 5 cm, 5 cm, 5 cm and 5 cm, 5 cm, 6 cm are within the perimeter limitations. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

8 If the two short sides are 5 cm and 6 cm, then the remaining side has to be less than 11 cm, which leaves 6 cm, 7 cm, 8 cm, 9 cm, and 10 cm as options. Since = 5, none of the possibilities will be within the perimeter limitations. Now look at situations in which 5 cm would be the long side. Look for integers less than 5 that when added together are greater than 5. There are four possibilities = 6; = 6; = 7; = 8. Therefore 2 cm, 4 cm, 5 cm; 3 cm, 3 cm, 5 cm; 3 cm, 4 cm, 5 cm; and 4 cm, 4 cm, 5 cm are within the given limitations. Make a list of all triangles that were within the given limitations cm, 5 cm, 5 cm 2. 2 cm, 5 cm, 5 cm 3. 2 cm, 5 cm, 6 cm 4. 3 cm, 5 cm, 5 cm 5. 3 cm, 5 cm, 6 cm 6. 3 cm, 5 cm, 7 cm 7. 4 cm, 5 cm, 5 cm 8. 4 cm, 5 cm, 6 cm 9. 4 cm, 5 cm, 7 cm cm, 5 cm, 5 cm cm, 5 cm, 6 cm cm, 4 cm, 5 cm cm, 3 cm, 5 cm cm, 4 cm, 5 cm cm, 4 cm, 5 cm Therefore, Shelbie can construct 15 unique triangles of which 7 are strictly isosceles and 1 is equilateral. 15. An obtuse angle is greater than 90, an acute angle is less than 90, and a right angle is equal to 90. Since the sum of the angles in a triangle is 180, at least two of the angles must be acute. Therefore, it is false that a triangle can be drawn with exactly one acute angle. 16. First, find the measure of the missing angle in the triangle. 180 ( ) = = 60 All the angles in the triangle are less than 90, so the triangle is an acute triangle. Next, the three angles in the triangle each measure 60, so the triangle is equiangular and equilateral. Therefore, the triangle is best described as an acute equilateral triangle. 17. According to the triangle inequality theorem, the sum of any two sides must be greater than the third side. Since the sum of 4 m and 4 m is greater than 7 m, the side lengths do form a triangle. A triangle with two equal sides is an isosceles triangle. Only one isosceles triangle with side lengths of 4 m, 4 m, and 7 m exists. Therefore, exactly one unique triangle exists with the given side lengths. 18. The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the third side. Since the two given sides have lengths of 20 inches and 29 inches, the third side, AC, must fit the following inequalities. AC < 20 inches + 29 inches = 49 inches and AC > 29 inches 20 inches = 9 inches Thus, 9 inches < AC < 49 inches. Of the answer choices given, 44 inches is the only choice that falls within this range. 19. The sum of the angles in a triangle is 180, so the angles do form a triangle. Since two of the three angles are congruent, the triangle is an isosceles triangle. An infinite number of isosceles triangles exist with different side lengths. Therefore, more than one triangle exists with the given angle measures. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

9 Therefore, more than one triangle exists with the given angle measures. 20. The sum of the angles in a triangle is 180. These angles add up to more than 180, so the angles do not form a triangle. Therefore, no triangle exists with the given angle measures. practice worksheet/9e4d8?cfid=1237a6d7 82b b4e4 a0242c11ee78&cftoken=0&apprnd= /9

GEOMETRY: TRIANGLES COMMON MISTAKES

GEOMETRY: TRIANGLES COMMON MISTAKES GEOMETRY: TRIANGLES COMMON MISTAKES 1 Geometry-Classifying Triangles How Triangles are Classified Types-Triangles are classified by Angles or Sides By Angles- Obtuse Triangles-triangles with one obtuse

More information

Preparation Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess My Rule Cards handout.

Preparation Prepare a set of standard triangle shapes for each student. The shapes are found in the Guess My Rule Cards handout. Classifying Triangles Student Probe How are triangles A, B, and C alike? How are triangles A, B, and C different? A B C Answer: They are alike because they each have 3 sides and 3 angles. They are different

More information

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA- (x₂-x₁)²+(y₂-y₁)² Find the distance between the points ( -3,2) and

More information

How Do You Measure a Triangle? Examples

How Do You Measure a Triangle? Examples How Do You Measure a Triangle? Examples 1. A triangle is a three-sided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints,

More information

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms. Quadrilaterals - Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals - Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,

More information

Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook

Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Objectives Use the triangle measurements to decide which side is longest and which angle is largest.

More information

Chapter 5.1 and 5.2 Triangles

Chapter 5.1 and 5.2 Triangles Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three non-collinear points are connected by segments. Each

More information

Geometry: Classifying, Identifying, and Constructing Triangles

Geometry: Classifying, Identifying, and Constructing Triangles Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral

More information

Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester

Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester CH. 4 Guided Notes, page 2 4.1 Apply Triangle Sum Properties triangle polygon

More information

Triangles can be classified by angles and sides. Write a good definition of each term and provide a sketch: Classify triangles by angles:

Triangles can be classified by angles and sides. Write a good definition of each term and provide a sketch: Classify triangles by angles: Chapter 4: Congruent Triangles A. 4-1 Classifying Triangles Identify and classify triangles by angles. Identify and classify triangles by sides. Triangles appear often in construction. Roofs sit atop a

More information

Invention of the plane geometrical formulae - Part II

Invention of the plane geometrical formulae - Part II International Journal of Computational Engineering Research Vol, 03 Issue, Invention of the plane geometrical formulae - Part II Mr. Satish M. Kaple Asst. Teacher Mahatma Phule High School, Kherda Jalgaon

More information

6.1 Basic Right Triangle Trigonometry

6.1 Basic Right Triangle Trigonometry 6.1 Basic Right Triangle Trigonometry MEASURING ANGLES IN RADIANS First, let s introduce the units you will be using to measure angles, radians. A radian is a unit of measurement defined as the angle at

More information

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem Name Period 10/22 11/1 Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle 10/22 Classify and Triangle Angle Theorems

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

Grade 4 - Module 4: Angle Measure and Plane Figures

Grade 4 - Module 4: Angle Measure and Plane Figures Grade 4 - Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. 1. measures less than By the Exterior Angle Inequality Theorem, the exterior angle ( ) is larger than

More information

All about those Triangles and Circles

All about those Triangles and Circles All about those Triangles and Circles 1BUTYPES OF TRIANGLES Triangle - A three-sided polygon. The sum of the angles of a triangle is 180 degrees. Isosceles Triangle - A triangle having two sides of equal

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

(c) What is the value of the digit 3 in this number? [1] What is the difference in the place values of the digits 2 and 6 in

(c) What is the value of the digit 3 in this number? [1] What is the difference in the place values of the digits 2 and 6 in Assessment Test for Singapore Primary Mathematics 4A Standards Edition This test covers material taught in Primary Mathematics 4A Standards Edition (http://www.singaporemath.com/) 1. Consider the number

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

Chapter 8 Geometry We will discuss following concepts in this chapter. Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

More information

Pre-Calculus II. 4.3 Right Angle Trigonometry

Pre-Calculus II. 4.3 Right Angle Trigonometry Pre-Calculus II 4.3 Right Angle Trigonometry y P=(x,y) y P=(x,y) 1 1 y x x x We construct a right triangle by dropping a line segment from point P perpendicular to the x-axis. So now we can view as the

More information

Selected practice exam solutions (part 5, item 2) (MAT 360)

Selected practice exam solutions (part 5, item 2) (MAT 360) Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On

More information

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1

The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1 47 Similar Triangles An overhead projector forms an image on the screen which has the same shape as the image on the transparency but with the size altered. Two figures that have the same shape but not

More information

Cumulative Test. 161 Holt Geometry. Name Date Class

Cumulative Test. 161 Holt Geometry. Name Date Class Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2

More information

55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.

55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points. Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

GEOMETRY FINAL EXAM REVIEW

GEOMETRY FINAL EXAM REVIEW GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.

More information

11-4 Areas of Regular Polygons and Composite Figures

11-4 Areas of Regular Polygons and Composite Figures 1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

More information

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

More information

Polygons are figures created from segments that do not intersect at any points other than their endpoints.

Polygons are figures created from segments that do not intersect at any points other than their endpoints. Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles

More information

Unit 3: Triangle Bisectors and Quadrilaterals

Unit 3: Triangle Bisectors and Quadrilaterals Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties

More information

Course 2 Summer Packet For students entering 8th grade in the fall

Course 2 Summer Packet For students entering 8th grade in the fall Course 2 Summer Packet For students entering 8th grade in the fall The summer packet is comprised of important topics upcoming eighth graders should know upon entering math in the fall. Please use your

More information

4. How many integers between 2004 and 4002 are perfect squares?

4. How many integers between 2004 and 4002 are perfect squares? 5 is 0% of what number? What is the value of + 3 4 + 99 00? (alternating signs) 3 A frog is at the bottom of a well 0 feet deep It climbs up 3 feet every day, but slides back feet each night If it started

More information

Section 7.1 Solving Right Triangles

Section 7.1 Solving Right Triangles Section 7.1 Solving Right Triangles Note that a calculator will be needed for most of the problems we will do in class. Test problems will involve angles for which no calculator is needed (e.g., 30, 45,

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: The point of intersection of the three medians of a triangle. Centroid Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

More information

Show that polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement.

Show that polygons are congruent by identifying all congruent corresponding parts. Then write a congruence statement. Triangles Show that polygons are congruent by identifying all congruent corresponding parts Then write a congruence statement 1 SOLUTION: All corresponding parts of the two triangles are congruent Therefore

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

Final Review Geometry A Fall Semester

Final Review Geometry A Fall Semester Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over

More information

Sum of the interior angles of a n-sided Polygon = (n-2) 180

Sum of the interior angles of a n-sided Polygon = (n-2) 180 5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a n-sided Polygon = (n-2) 180 What you need to know: How to use the formula

More information

Topics Covered on Geometry Placement Exam

Topics Covered on Geometry Placement Exam Topics Covered on Geometry Placement Exam - Use segments and congruence - Use midpoint and distance formulas - Measure and classify angles - Describe angle pair relationships - Use parallel lines and transversals

More information

/27 Intro to Geometry Review

/27 Intro to Geometry Review /27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Click the mouse button

More information

Which two rectangles fit together, without overlapping, to make a square?

Which two rectangles fit together, without overlapping, to make a square? SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has

More information

Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes

Tennessee Mathematics Standards 2009-2010 Implementation. Grade Six Mathematics. Standard 1 Mathematical Processes Tennessee Mathematics Standards 2009-2010 Implementation Grade Six Mathematics Standard 1 Mathematical Processes GLE 0606.1.1 Use mathematical language, symbols, and definitions while developing mathematical

More information

Honors Geometry Final Exam Study Guide

Honors Geometry Final Exam Study Guide 2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

More information

" Angles ABCand DEFare congruent

 Angles ABCand DEFare congruent Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)

More information

2. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisector for each type of triangle

2. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisector for each type of triangle Using a compass and straight edge (ruler) construct the angle bisectors, perpendicular bisectors, altitudes, and medians for 4 different triangles; a, Isosceles Triangle, Scalene Triangle, and an. The

More information

100 Math Facts 6 th Grade

100 Math Facts 6 th Grade 100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

More information

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

More information

Overview of Geometry Map Project

Overview of Geometry Map Project Overview of Geometry Map Project The goal: To demonstrate your understanding of geometric vocabulary, you will be designing and drawing a town map that incorporates many geometric key terms. The project

More information

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

More information

Constructing Symmetrical Shapes

Constructing Symmetrical Shapes 07-NEM5-WBAns-CH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2-D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete

More information

Discovering Math: Exploring Geometry Teacher s Guide

Discovering Math: Exploring Geometry Teacher s Guide Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional

More information

Chapter 5: Relationships within Triangles

Chapter 5: Relationships within Triangles Name: Chapter 5: Relationships within Triangles Guided Notes Geometry Fall Semester CH. 5 Guided Notes, page 2 5.1 Midsegment Theorem and Coordinate Proof Term Definition Example midsegment of a triangle

More information

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE? MATH 206 - Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of

More information

3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)

3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks) EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

I Perimeter, Area, Learning Goals 304

I Perimeter, Area, Learning Goals 304 U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

More information

ABC is the triangle with vertices at points A, B and C

ABC is the triangle with vertices at points A, B and C Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry - symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the

More information

UNIT 8 RIGHT TRIANGLES NAME PER. I can define, identify and illustrate the following terms

UNIT 8 RIGHT TRIANGLES NAME PER. I can define, identify and illustrate the following terms UNIT 8 RIGHT TRIANGLES NAME PER I can define, identify and illustrate the following terms leg of a right triangle short leg long leg radical square root hypotenuse Pythagorean theorem Special Right Triangles

More information

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

More information

Bisections and Reflections: A Geometric Investigation

Bisections and Reflections: A Geometric Investigation Bisections and Reflections: A Geometric Investigation Carrie Carden & Jessie Penley Berry College Mount Berry, GA 30149 Email: ccarden@berry.edu, jpenley@berry.edu Abstract In this paper we explore a geometric

More information

Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter

Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter Heron s Formula Lesson Summary: Students will investigate the Heron s formula for finding the area of a triangle. The lab has students find the area using three different methods: Heron s, the basic formula,

More information

Unit 2, Activity 2, One-half Inch Grid

Unit 2, Activity 2, One-half Inch Grid Unit 2, Activity 2, One-half Inch Grid Blackline Masters, Mathematics, Grade 8 Page 2-1 Unit 2, Activity 2, Shapes Cut these yellow shapes out for each pair of students prior to class. The labels for each

More information

Angles and Algebra Examples

Angles and Algebra Examples Angles and Algebra Examples 1. A protractor can be used to measure angles as shown below. Point out that ABC is the supplement of DBC. C D 2. ABC measures 60 o. DBC measures 120 o. What is the sum of the

More information

5.1 Midsegment Theorem and Coordinate Proof

5.1 Midsegment Theorem and Coordinate Proof 5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle - A midsegment of a triangle is a segment that connects

More information

Math Common Core Standards Fourth Grade

Math Common Core Standards Fourth Grade Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

More information

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 9) 179 Trigonometry Chapters 1 & 2 Test 1 Name Provide an appropriate response. 1) Find the supplement of an angle whose measure is 7. Find the measure of each angle in the problem. 2) Perform the calculation.

More information

Name Period Right Triangles and Trigonometry Section 9.1 Similar right Triangles

Name Period Right Triangles and Trigonometry Section 9.1 Similar right Triangles Name Period CHAPTER 9 Right Triangles and Trigonometry Section 9.1 Similar right Triangles Objectives: Solve problems involving similar right triangles. Use a geometric mean to solve problems. Ex. 1 Use

More information

Chapter 4: Congruent Triangles

Chapter 4: Congruent Triangles Name: Chapter 4: Congruent Triangles Guided Notes Geometry Fall Semester 4.1 Apply Triangle Sum Properties CH. 4 Guided Notes, page 2 Term Definition Example triangle polygon sides vertices Classifying

More information

25 The Law of Cosines and Its Applications

25 The Law of Cosines and Its Applications Arkansas Tech University MATH 103: Trigonometry Dr Marcel B Finan 5 The Law of Cosines and Its Applications The Law of Sines is applicable when either two angles and a side are given or two sides and an

More information

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,

More information

Geometry Chapter 5 Relationships Within Triangles

Geometry Chapter 5 Relationships Within Triangles Objectives: Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 To use properties of midsegments to solve problems. To use properties of perpendicular bisectors and angle bisectors. To identify

More information

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points

More information

Q1. Lindy has 4 triangles, all the same size. She uses them to make a star. Calculate the perimeter of the star. 2 marks.

Q1. Lindy has 4 triangles, all the same size. She uses them to make a star. Calculate the perimeter of the star. 2 marks. Q1. Lindy has 4 triangles, all the same size. She uses them to make a star. Calculate the perimeter of the star. Page 1 of 16 Q2. Liam has two rectangular tiles like this. He makes this L shape. What is

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information

Objectives. Cabri Jr. Tools

Objectives. Cabri Jr. Tools ^Åíáîáíó=NU Objectives To investigate the special properties of an altitude, a median, and an angle bisector To reinforce the differences between an altitude, a median, and an angle bisector Cabri Jr.

More information

Assessment For The California Mathematics Standards Grade 3

Assessment For The California Mathematics Standards Grade 3 Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

More information

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter

More information

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse

Pythagoras Theorem. Page I can... 1... identify and label right-angled triangles. 2... explain Pythagoras Theorem. 4... calculate the hypotenuse Pythagoras Theorem Page I can... 1... identify and label right-angled triangles 2... eplain Pythagoras Theorem 4... calculate the hypotenuse 5... calculate a shorter side 6... determine whether a triangle

More information

1 Solution of Homework

1 Solution of Homework Math 3181 Dr. Franz Rothe February 4, 2011 Name: 1 Solution of Homework 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases,

More information

Grade 3 FCAT 2.0 Mathematics Sample Answers

Grade 3 FCAT 2.0 Mathematics Sample Answers Grade FCAT 2.0 Mathematics Sample Answers This booklet contains the answers to the FCAT 2.0 Mathematics sample questions, as well as explanations for the answers. It also gives the Next Generation Sunshine

More information

Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. 42. The sum of the measures of the angles of a triangle is 180. Therefore, The sine of an angle

More information

NEW MEXICO Grade 6 MATHEMATICS STANDARDS

NEW MEXICO Grade 6 MATHEMATICS STANDARDS PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

More information

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4 of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

More information

Classifying Lesson 1 Triangles

Classifying Lesson 1 Triangles Classifying Lesson 1 acute angle congruent scalene Classifying VOCABULARY right angle isosceles Venn diagram obtuse angle equilateral You classify many things around you. For example, you might choose

More information

2006 Geometry Form A Page 1

2006 Geometry Form A Page 1 2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches

More information

11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry 11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

More information

2004 Solutions Ga lois Contest (Grade 10)

2004 Solutions Ga lois Contest (Grade 10) Canadian Mathematics Competition An activity of The Centre for Education in Ma thematics and Computing, University of W aterloo, Wa terloo, Ontario 2004 Solutions Ga lois Contest (Grade 10) 2004 Waterloo

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

Geometry of 2D Shapes

Geometry of 2D Shapes Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

More information

Right Triangles 4 A = 144 A = 16 12 5 A = 64

Right Triangles 4 A = 144 A = 16 12 5 A = 64 Right Triangles If I looked at enough right triangles and experimented a little, I might eventually begin to notice a relationship developing if I were to construct squares formed by the legs of a right

More information

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same. Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

Right Triangles and Quadrilaterals

Right Triangles and Quadrilaterals CHATER. RIGHT TRIANGLE AND UADRILATERAL 18 1 5 11 Choose always the way that seems the best, however rough it may be; custom will soon render it easy and agreeable. ythagoras CHATER Right Triangles and

More information

Heron Triangles. by Kathy Temple. Arizona Teacher Institute. Math Project Thesis

Heron Triangles. by Kathy Temple. Arizona Teacher Institute. Math Project Thesis Heron Triangles by Kathy Temple Arizona Teacher Institute Math Project Thesis In partial fulfillment of the M.S. Degree in Middle School Mathematics Teaching Leadership Department of Mathematics University

More information

Lesson 12.1 Skills Practice

Lesson 12.1 Skills Practice Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle A circle is a collection of points on the same plane

More information