COLLEGE GEOMETRY SAMPLE QUESTIONS. Contents 1. Elementary Geometry 1 2. Coordinate Geometry 4

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "COLLEGE GEOMETRY SAMPLE QUESTIONS. Contents 1. Elementary Geometry 1 2. Coordinate Geometry 4"

Transcription

1 COLLEGE GEOMETRY SAMPLE QUESTIONS Contents 1. Elementary Geometry 1 2. Coordinate Geometry 4 1. Elementary Geometry 1a. Two sides of a triangle are a = 8 and b = 6, the angle α (opposite to the side a) is 45. Calculate the missing side. Find the area of the triangle. 1b. Two sides of a triangle are a = 6 and b = 3, the angle α (opposite to the side a) is 60. Calculate the missing side and angles. Find the area of the triangle. 1c. Two sides of a triangle and the angle enclosed by them are given: a=3, b=4 and γ = 60. a) Find the missing side. b) Calculate the area of the triangle. c) Calculate the radius of the circumscribed circle. 1d. Three sides of a triangle are given: a=3, b=4 and c= 13. a) Find the angle γ opposite to the side c. b) Calculate the area of the triangle. 1e. The sides of a triangle are a = 5, b = 12 and c = 13. Calculate the angle opposite to the side c. 1f. Three sides of a triangle are given: 13, 13 and 24. a) Calculate the heights and the area of the triangle! b) Calculate the biggest angle of the triangle! c) Calculate the radius of the inscribed circle of the triangle! 2a. In a right triangle the longest side AB is 5. The leg BC is 3. Calculate the missing leg. Find the radius of the circumscribed circle. Compute the height belongig to the hypothenuse. 2b. The area of a right angle triangle is 30, the sum of the legs is 17. Calculate the sides of the triangle. 1

2 COLLEGE GEOMETRY SAMPLE QUESTIONS 2 2c. The radius of the circumscribed circle around a right triangle is 5, one of the legs is 6. What is the area of the triangle. 3a. In a symmetrical trapezoid the lenght of the shorter parallel base is 10. The common lenght of the legs is 5 and the height is 4. What is the area of the trapezoid? 3b. Three sides in a symmetrical trapezoid are of lenght 10, the fourth side has lenght 20. Calculate the area of the trapezoid. 3c. In a symmetrical trapezium the inclination angle of the diagonal to the longer parallel base is 45, the lenght of the diagonal is 10. What is the area of the trapezium? 3d. The longest base of a symmetrical trapezoid is 20, the length of the legs is 5, the height is 3. a) Calculate the area of the trapezoid! b) Calculate the angles of the trapezoid! 3e. The longer diagonal of a rhombus is given: 12, and one of the angle of the rhombus is 60 a) Calculate the area of the rhombus! b) Calculate the length of the sides of the rhombus! 3f. The perimeter of a rhombus is 40, its area is 96. What are the angles, sides, and diagonals of the rhombus? 4a. Calculate the common length of the sides of a regular 10-gon inscribed in the unit circle. 4b. The length of the side of a regular 6-gon is given: 8. a) Calculate the angles of the polygon! b) What is the length of the shorter diagonal? c) What is the area of the polygon? 4c. The lenght of the side of a regular 8-gon is given: 6. Calculate the area of the polygon. 5a. Let a circle with radius 2 be given. The distance between the point P and the center of the circle is 4. Calculate the common length of the tangent segments from P to the given circle and find the length of the shorter arc along the circle between the contact points A and B. 5b. Let a circle with radius 3 be given. The distance between the point P and the center of the circle is 6. Calculate the common length of the tangent segments from P to the given circle and find the length of the shorter arc along the circle between the contact points A and B.

3 COLLEGE GEOMETRY SAMPLE QUESTIONS 3 5c. Two circles of radius 10 intersect each other. The distance of the their centers is 16. Calculate the area of the common part of the two circles! 5d. Two circles of radius 5 intersect each other. The distance of the their centers is 8. Calculate the area of the common part of the two circles!

4 COLLEGE GEOMETRY SAMPLE QUESTIONS 4 2. Coordinate Geometry 1a. Compute the distance between the points A(4, 1) and B(1, 1). Find the coordinates of the midpoint of the segment AB. 1b. Let the points A( 3, 2), B(2, 3) and C(1, 2) be given. Compute the angle at A in the triangle ABC. Find the area of the triangle. compute the sides of the triangle, use the cosine rule BC 2 = AB 2 + AC 2 2 AB AC cos A to calculate the angle at A. 1c. Let the points A( 1, 1), B(1, 3) and C(3, 2) be given. Find the coordinates of the missing point D of the parallelogram ABCD. How many solutions we have? 2a. Let the points A(4, 1), B(1, 1) and C(1, 2) be given. Find the equation of the line passing through the points A and B, passing through the point C and parallel to the line AB, passing through the point C and perpendicular to the line AB. Find the distance between the point C and the line AB. 2b. Find the equation of the line passing through the point C(3, 2) and parallel to y = 3x + 5 perpendicular to y = 2 3 x c. Find the common point of the lines y = 2x + 3 and y = 3x 8. 3a. Find the common points of the line y = 2x 3 and the circle (x 1) 2 + (y + 1) 2 = 25. 3b. Find the equation of the tangent lines to the circle (x 1) 2 +(y+1) 2 = 16 which are parallel to y = 2x 3. write the equation of the line passing through C and perpendicular to y = 2x 3, the common points of the line in the previous step and the given circle are the contact points of the tangent lines. 3c. Find the equation of the tangent line to the circle (x 1) 2 +(y +1) 2 = 25 at the point P (4, 3).

5 COLLEGE GEOMETRY SAMPLE QUESTIONS 5 write the equation of the line passing through C and P, write the equation of the line passing through P and perpendicular to the line CP. 4a. Find the common points of the circles (x + 1) 2 + (y 1) 2 = 5 and x 2 + y 2 = 1 4b. Find the equation of the tangent lines to the circle (x 1) 2 +(y+1) 2 = 16 from the point P (3, 5). calculate the coordinates of the midpoint of the segment CP : M(2, 2). calculate the distance between C and M: 10, the common points of the circles (x 1) 2 + (y + 1) 2 = 16 and (x 2) 2 + (y 2) 2 = 10 will be the contact points of the tangent lines. 4c. Let the points A( 1, 1), B(1, 3) and C(3, 2) be given. Find the equation of the circumscribed circle of the triangle ABC. 5. Explain why the following method is working well. Excercise: find the common points of the circles (x 1) 2 + (y + 1) 2 = 16 and (x 2) 2 + (y 2) 2 = 10. Solution. (displacement-solution-displacement) We are going to find the common points of the circles Taking the difference we have Therefore and, consequently, (x + 1) 2 + (y + 3) 2 = 16 x 2 + y 2 = 10. x + 3y = 2. (2 + 3y) 2 + y 2 = 10 5y 2 + 6y 3 = 0 y 1 = , y 2 = x 1 = (2 + 3y 1 ), x 2 = (2 + 3y 2 ). The solutions of the original problem are A(x 1 + 2, y 1 + 2) and B(x 2 + 2, y 2 + 2)

CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session. Geometry, 17 March 2012 CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

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

Geometry Final Exam Review Worksheet

Geometry Final Exam Review Worksheet Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.

More information

1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.

1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X. 1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides

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

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

Chapters 6 and 7 Notes: Circles, Locus and Concurrence

Chapters 6 and 7 Notes: Circles, Locus and Concurrence Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of

More information

0810ge. Geometry Regents Exam 0810

0810ge. Geometry Regents Exam 0810 0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify

More information

Properties of Special Parallelograms

Properties of Special Parallelograms Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then

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

Chapter 6 Notes: Circles

Chapter 6 Notes: Circles Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment

More information

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,

More information

Area. Area Overview. Define: Area:

Area. Area Overview. Define: Area: Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

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

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle. DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent

More information

PERIMETERS AND AREAS

PERIMETERS AND AREAS PERIMETERS AND AREAS 1. PERIMETER OF POLYGONS The Perimeter of a polygon is the distance around the outside of the polygon. It is the sum of the lengths of all the sides. Examples: The perimeter of this

More information

39 Symmetry of Plane Figures

39 Symmetry of Plane Figures 39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

More information

4.1 Euclidean Parallelism, Existence of Rectangles

4.1 Euclidean Parallelism, Existence of Rectangles Chapter 4 Euclidean Geometry Based on previous 15 axioms, The parallel postulate for Euclidean geometry is added in this chapter. 4.1 Euclidean Parallelism, Existence of Rectangles Definition 4.1 Two distinct

More information

Analytical Geometry (4)

Analytical Geometry (4) Analytical Geometry (4) Learning Outcomes and Assessment Standards Learning Outcome 3: Space, shape and measurement Assessment Standard As 3(c) and AS 3(a) The gradient and inclination of a straight line

More information

NCERT. Area of the circular path formed by two concentric circles of radii. Area of the sector of a circle of radius r with central angle θ =

NCERT. Area of the circular path formed by two concentric circles of radii. Area of the sector of a circle of radius r with central angle θ = AREA RELATED TO CIRCLES (A) Main Concepts and Results CHAPTER 11 Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle

More information

Math 531, Exam 1 Information.

Math 531, Exam 1 Information. Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)

More information

Circle Name: Radius: Diameter: Chord: Secant:

Circle Name: Radius: Diameter: Chord: Secant: 12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane

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

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

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

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name: GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

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

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

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

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 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, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

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

Geometry: Euclidean. Through a given external point there is at most one line parallel to a

Geometry: Euclidean. Through a given external point there is at most one line parallel to a Geometry: Euclidean MATH 3120, Spring 2016 The proofs of theorems below can be proven using the SMSG postulates and the neutral geometry theorems provided in the previous section. In the SMSG axiom list,

More information

Geometry SOL G.11 G.12 Circles Study Guide

Geometry SOL G.11 G.12 Circles Study Guide Geometry SOL G.11 G.1 Circles Study Guide Name Date Block Circles Review and Study Guide Things to Know Use your notes, homework, checkpoint, and other materials as well as flashcards at quizlet.com (http://quizlet.com/4776937/chapter-10-circles-flashcardsflash-cards/).

More information

Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!

Chapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret

More information

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2

The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 s s rectangle: A = l w parallelogram: A = b h h b triangle:

More information

Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18

Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18 Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,

More information

Review for Final - Geometry B

Review for Final - Geometry B Review for Final - Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters

More information

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?

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

Geometry Module 4 Unit 2 Practice Exam

Geometry Module 4 Unit 2 Practice Exam Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

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

10-4 Inscribed Angles. Find each measure. 1.

10-4 Inscribed Angles. Find each measure. 1. Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what

More information

SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses

SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning

More information

GEOMETRY CONCEPT MAP. Suggested Sequence:

GEOMETRY CONCEPT MAP. Suggested Sequence: CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

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 Regents Review

Geometry Regents Review Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

More information

SMT 2014 Geometry Test Solutions February 15, 2014

SMT 2014 Geometry Test Solutions February 15, 2014 SMT 014 Geometry Test Solutions February 15, 014 1. The coordinates of three vertices of a parallelogram are A(1, 1), B(, 4), and C( 5, 1). Compute the area of the parallelogram. Answer: 18 Solution: Note

More information

A. 3y = -2x + 1. y = x + 3. y = x - 3. D. 2y = 3x + 3

A. 3y = -2x + 1. y = x + 3. y = x - 3. D. 2y = 3x + 3 Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x - 1 D. y = 3x + 1

More information

The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach

The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach Lesson Summary: This lesson is for more advanced geometry students. In this lesson,

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

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. 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

Geometry Enduring Understandings Students will understand 1. that all circles are similar.

Geometry Enduring Understandings Students will understand 1. that all circles are similar. High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,

More information

Geometry, Final Review Packet

Geometry, Final Review Packet Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a

More information

Chapter 11 Area of Quadrilateral

Chapter 11 Area of Quadrilateral 75 Chapter 11 11.1 Quadrilateral A plane figure bounded by four sides is known as a quadrilateral. The straight line joining the opposite corners is called its diagonal. The diagonal divides the quadrilateral

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

Each pair of opposite sides of a parallelogram is congruent to each other.

Each pair of opposite sides of a parallelogram is congruent to each other. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

More information

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

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

New York State Student Learning Objective: Regents Geometry

New York State Student Learning Objective: Regents Geometry New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students

More information

Situation: Proving Quadrilaterals in the Coordinate Plane

Situation: Proving Quadrilaterals in the Coordinate Plane Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra

More information

CIRCLE COORDINATE GEOMETRY

CIRCLE COORDINATE GEOMETRY CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle

More information

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

More information

Chapter 6 Quiz. Section 6.1 Circles and Related Segments and Angles

Chapter 6 Quiz. Section 6.1 Circles and Related Segments and Angles Chapter 6 Quiz Section 6.1 Circles and Related Segments and Angles (1.) TRUE or FALSE: The center of a circle lies in the interior of the circle. For exercises 2 4, use the figure provided. (2.) In O,

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

The Four Centers of a Triangle. Points of Concurrency. Concurrency of the Medians. Let's Take a Look at the Diagram... October 25, 2010.

The Four Centers of a Triangle. Points of Concurrency. Concurrency of the Medians. Let's Take a Look at the Diagram... October 25, 2010. Points of Concurrency Concurrent lines are three or more lines that intersect at the same point. The mutual point of intersection is called the point of concurrency. Example: x M w y M is the point of

More information

Geometry A Solutions. Written by Ante Qu

Geometry A Solutions. Written by Ante Qu Geometry A Solutions Written by Ante Qu 1. [3] Three circles, with radii of 1, 1, and, are externally tangent to each other. The minimum possible area of a quadrilateral that contains and is tangent to

More information

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

www.sakshieducation.com

www.sakshieducation.com LENGTH OF THE PERPENDICULAR FROM A POINT TO A STRAIGHT LINE AND DISTANCE BETWEEN TWO PAPALLEL LINES THEOREM The perpendicular distance from a point P(x 1, y 1 ) to the line ax + by + c 0 is ax1+ by1+ c

More information

San Jose Math Circle February 14, 2009 CIRCLES AND FUNKY AREAS - PART II. Warm-up Exercises

San Jose Math Circle February 14, 2009 CIRCLES AND FUNKY AREAS - PART II. Warm-up Exercises San Jose Math Circle February 14, 2009 CIRCLES AND FUNKY AREAS - PART II Warm-up Exercises 1. In the diagram below, ABC is equilateral with side length 6. Arcs are drawn centered at the vertices connecting

More information

Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem.

Law of Cosines. If the included angle is a right angle then the Law of Cosines is the same as the Pythagorean Theorem. Law of Cosines In the previous section, we learned how the Law of Sines could be used to solve oblique triangles in three different situations () where a side and two angles (SAA) were known, () where

More information

MENSURATION. Definition

MENSURATION. Definition MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

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

4. An isosceles triangle has two sides of length 10 and one of length 12. What is its area?

4. An isosceles triangle has two sides of length 10 and one of length 12. What is its area? 1 1 2 + 1 3 + 1 5 = 2 The sum of three numbers is 17 The first is 2 times the second The third is 5 more than the second What is the value of the largest of the three numbers? 3 A chemist has 100 cc of

More information

The measure of an arc is the measure of the central angle that intercepts it Therefore, the intercepted arc measures

The measure of an arc is the measure of the central angle that intercepts it Therefore, the intercepted arc measures 8.1 Name (print first and last) Per Date: 3/24 due 3/25 8.1 Circles: Arcs and Central Angles Geometry Regents 2013-2014 Ms. Lomac SLO: I can use definitions & theorems about points, lines, and planes to

More information

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points. 6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

More information

CHAPTER 1. LINES AND PLANES IN SPACE

CHAPTER 1. LINES AND PLANES IN SPACE CHAPTER 1. LINES AND PLANES IN SPACE 1. Angles and distances between skew lines 1.1. Given cube ABCDA 1 B 1 C 1 D 1 with side a. Find the angle and the distance between lines A 1 B and AC 1. 1.2. Given

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

The Area is the width times the height: Area = w h

The Area is the width times the height: Area = w h Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what

More information

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

Perimeter and area formulas for common geometric figures:

Perimeter and area formulas for common geometric figures: Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,

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

Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper

Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving

More information

Quadrilateral Geometry. Varignon s Theorem I. Proof 10/21/2011 S C. MA 341 Topics in Geometry Lecture 19

Quadrilateral Geometry. Varignon s Theorem I. Proof 10/21/2011 S C. MA 341 Topics in Geometry Lecture 19 Quadrilateral Geometry MA 341 Topics in Geometry Lecture 19 Varignon s Theorem I The quadrilateral formed by joining the midpoints of consecutive sides of any quadrilateral is a parallelogram. PQRS is

More information

Radius, diameter, circumference, π (Pi), central angles, Pythagorean relationship. about CIRCLES

Radius, diameter, circumference, π (Pi), central angles, Pythagorean relationship. about CIRCLES Grade 9 Math Unit 8 : CIRCLE GEOMETRY NOTES 1 Chapter 8 in textbook (p. 384 420) 5/50 or 10% on 2011 CRT: 5 Multiple Choice WHAT YOU SHOULD ALREADY KNOW: Radius, diameter, circumference, π (Pi), central

More information

Geometry EOC Practice Test #2

Geometry EOC Practice Test #2 Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply

More information

Visualizing Triangle Centers Using Geogebra

Visualizing Triangle Centers Using Geogebra Visualizing Triangle Centers Using Geogebra Sanjay Gulati Shri Shankaracharya Vidyalaya, Hudco, Bhilai India http://mathematicsbhilai.blogspot.com/ sanjaybhil@gmail.com ABSTRACT. In this paper, we will

More information

Lesson 3.1 Duplicating Segments and Angles

Lesson 3.1 Duplicating Segments and Angles Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each

More information

Geometry. Higher Mathematics Courses 69. Geometry

Geometry. Higher Mathematics Courses 69. Geometry The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

More information

Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.

Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. Sec 1.1 CC Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have

More information

Lesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes

Lesson 21. Chapter 2: Perimeter, Area & Volume. Lengths and Areas of Rectangles, Triangles and Composite Shapes ourse: HV Lesson hapter : Perimeter, rea & Volume Lengths and reas of Rectangles, Triangles and omposite Shapes The perimeter of a shape is the total length of its boundary. You can find the perimeter

More information

Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math. Semester 1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

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

7. 6 Justifying Constructions

7. 6 Justifying Constructions 31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information