# Final Review Problems Geometry AC Name

Save this PDF as:

Size: px
Start display at page:

Download "Final Review Problems Geometry AC Name"

## Transcription

1 Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x-6. Find the measure of the angles. State the theorem(s) that support your equation. x = In, m = 30 and the exterior angle at is 120. Which is the longest side of the triangle? State the theorem(s) that support your equation. 3. In the diagram,. If is twice as large as E, find E. x = 30 E 4. In, is twice the measure of and the exterior angle at vertex measures 120. What is the measure of? State the theorem(s) that support your equation. < = 40

2 5. The measures of the three angles of a triangle are in the ratio of 1:4:5. What is the number of degrees in the smallest angle? State the theorem(s) that support your equation. x = The measure of the vertex angle of an isosceles triangle is twice the measure of the base angle. Find the measure of a base angle. State the theorem(s) that support your equation. x = In the diagram of, bisects and E bisects. If the measure of E = 70 and the measure of = 40, find m. Explain. < = 40 E 8. In an isosceles right triangle, the measure of one acute angle is 2x+5. Find the value of x. State the theorem(s) that support your equation. x = 20

3 9. In the diagram, E = 5x+20 and E = 3x+60. Find x. State the theorem(s) that support your equation. x = 20 E 10. If each base angle of an isosceles triangle is 15 more than the vertex angle, find the measure of the vertex angle. x = In the diagram of,. If = 80 and = x, find the value of x. State the theorem(s) that support your equation. x = The angles of a triangle are in the ratio 3:5:7. Find the measure of the smallest angle. k = 12 < = 36

4 13. In the diagram,. If = 2x+18 and = 4x-18, find the value of x. State the theorem(s) that support your equation. x = Which set of numbers can represent the lengths of the sides of a triangle? State the theorem(s) that support your equation. a. 3, 3, 6 b. 3, 4, 7 c. 4, 7, 10 d. 4, 4, In PQR, P = 51 and Q = 57. Which expression is true? State the theorem(s) that support your equation. a. QR>PQ b. PR> PQ c. PQ=QR d. PQ>QR PRLLEL LINES 16. In the diagram EF, x = 70 and y = 105. Find the measure of z. State the theorem(s) that support your equation. x = 70, y = 105, z = 35 x y E z F

5 17. In the diagram,. If EF = 65 and GHF = 45, find EGH. State the theorem(s) that support your equation. E <EGH = 110 G F H 18. In the diagram,, E, = 2x, E = 3x. Find the value of x. State the theorem(s) that support your equation. E x = In the diagram,. If GH = 2x+10 and GH = 3x-20. Find the value of x. State the theorem(s) that support your equation. E G x = 38 H 20. In the diagram, & intersect at E, and & are drawn. If, E = 100 and E = 30, find E. < = 30; < = 50 F E

6 21. In the diagram, 1 and 2 are supplementary. Which is always true? State the theorem(s) that support your equation. p a. l p b. l m 1 c. l m d. m p l QURILTERLS 2 m 22. Which statement is FLSE? a. square is a rectangle b. square is a rhombus. c. rhombus is a square. d. rectangle is a parallelogram. 23. Which figure does NOT always have congruent diagonals? a. Rectangle b. Isosceles trapezoid c. Square d. Rhombus 24. If the diagonals of a quadrilateral are perpendicular and NOT congruent, the quadrilateral may be a(n). a. Rhombus b. Rectangle c. Isosceles trapezoid d. Square 25. Which statement is always true? a. The diagonals of a parallelogram are congruent. b. The diagonals of a parallelogram are perpendicular. c. The diagonals of a parallelogram bisect the angles. d. The diagonals of a parallelogram bisect each other.

7 26. The length of the shorter diagonal,, of rhombus is 8 and = 60. Find the length of a side of the rhombus. State the theorem(s) that support your equation. = In, is on, E is on, and E. If E = 8, find. = The sides of a triangle are 6, 8, 10. What is the perimeter of the triangle formed by joining the midpoints of these sides? What is type of triangle is it? What is the area of the triangle? State the theorem(s) that support your equation. P = 12; right triangle; = In the diagram, equilateral has a perimeter of 18. Points R, S, T are midpoints of the sides. What is the length of RS? = 6; RS = 3 R S T

8 30. In rhombus,, = 4x-2 and = 3x+3. Find x. State the theorem(s) that support your equation. x = In parallelogram PQRS, Q: R = 1:4. Find m Q. State the theorem(s) that support your equation. <Q = In parallelogram, = 60. Find m. State the theorem(s) that support your equation. < = In parallelogram, = (3x-40) and = (7x-100). Find x. x = 15

9 34. In quadrilateral, = 120, = 82 and = 93. Find m. State the theorem(s) that support your equation. < = The diagonals of a rhombus are 24 and 10. Find the length of a side. State the theorem(s) that support your equation In rectangle, = 3x-15 and = 7x-55. Find x. State the theorem(s) that support your equation. x = In the diagram of rhombus, = 50. Find m. State the theorem(s) that support your equation. x = 65

10 38. In rectangle, & intersect at point E. If E = 20 and = 2x+30, find x. State the theorem(s) that support your equation. x = The length of a rectangle is three times its width, and the perimeter is 32. Find the area of the rectangle. = In the diagram of rhombus, = 80. Find m. State the theorem(s) that support your equation. < = The lengths of the bases of a trapezoid are 4 and 8. If the length of the altitude is 3, find the area of the trapezoid. = 18

11 42. In the diagram, is equilateral and EF is a rhombus. If is the midpoint of and the perimeter of is 12, what is the perimeter of EF? State the theorem(s) that support your equation. P = 8 E F 43. What is the number of degrees in the measure of each exterior angle of a regular polygon of 18 sides? State the theorem(s) that support your equation. n = The lengths of the bases of an isosceles trapezoid are 7 and 15. Each leg makes an angle of 45 with the longer base. Find the length of the altitude x = 4, leg x = 4 2, and the median of the trapezoid x = If x+15 and 2x+27 represent the number of degrees in the measures of two consecutive angles of a parallelogram, find the value of x. State the theorem(s) that support your equation. x = 46

12 SIMILR POLYGONS 46. The lengths of the side of a triangle are 2, 5, and 6. If the length of the longest side of a similar triangle is 18, find the perimeter of the larger triangle. P = In the diagram of, is on and E is on, such that E. If = 6, = 4 and = 15, find E. State the theorem(s) that support your equation. x = 9; E = 6 E 48. In the diagram of, E. If = 10, = 6 and E = 7.5, find. State the theorem(s) that support your equation. = 12.5 E 49. What positive number is the mean proportional (geometric mean) between 4 and 9? x = 6

13 50. The lengths of the side of a triangle are 5, 7, and 8. If the longest side of a similar triangle is 24, find the perimeter of the larger triangle. P = The lengths of corresponding sides of two similar polygons are in the ratio 2:5. If the perimeter of the larger polygon is 100, what is the perimeter of the smaller polygon? State the theorem(s) that support your equation. P = In, is a point on, E is a point on and E. If = 4, = 6, and = 9, find E. E = In the diagram, E,, = 4, E = 3 and = 6. Find the length of. State the theorem(s) that support your equation. = 8 E

14 54. In the, E joins points and E on and, respectively. E and E is one-fourth as long as. The ratio of the perimeter of E to the perimeter of is a b. 1 2 c d. 1 4 RIGHT TRINGLES 55. The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments of lengths 3 and 12. What is the length of the altitude? State the theorem(s) that support your equation. a. 36 b. 18 c. 6 d If the ratio of the corresponding sides of two similar triangles is 4:9, then the ratio of their perimeters is a. 16:81 b. 8:27 c. 4:9 d 2:3 57. Which polygons are LWYS similar? Why? a. Equilateral triangles; all congruent angles b. Parallelograms c. Trapezoids d. Rectangles 58. In square, the length of a side is 3. Find the length of. = In right, is the altitude to hypotenuse. If = 6 and = 9, find. x = 4

15 60. In right, is the altitude to hypotenuse. If = 3 and = 9, find. = The length of a diagonal of a square is5 2. What is the length of a side? s = The length of a side of a square is 2. What is the length of the diagonal? d = The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 9. Find the length of the altitude. State the theorem(s) that support your equation. x = In a right triangle, one leg is 7 and the hypotenuse is 10. Find the length of the other leg. State the theorem(s) that support your equation. b = 51

16 65. The diagonals of a rhombus have lengths of 8 and 6. Find the length of a side of the rhombus In rectangle, = 12 and = 16. Find. State the theorem(s) that support your equation therefore, In square, the length of a side is 3. Find the length of. x = In right, altitude is drawn to the hypotenuse. If = 4 and = 5, find. State the theorem(s) that support your equation. x = In right, is a right angle. ltitude bisects the hypotenuse at. If = 10, find. State the theorem(s) that support your equation. x = 5

17 70. Which set of numbers could be the lengths of the sides of a right triangle? State the theorem(s) that support your equation. a. 2, 6, 40 b. 2, 18, 20 c. 4, 6, 40 d. 4, 36, rectangle has a diagonal of length 10 and one side of length 6. What is the perimeter of the rectangle? P = 28; triangle 72. In the diagram, altitude FG is drawn in EF. If E = 8, G = 4 and E = 60, what is the length of EF? EF = 8 F 73. onstruct the median of a triangle. G E 74. onstruct a triangle. 75. onstruct a triangle. 76. onstruct a rhombus with a 30 angle. 77. onstruct a trapezoid with a 30 angle and a 135 degree angle. 78. onstruct the circumscribed circle of an obtuse isosceles triangle. Perp. is of sides 79. onstruct all three altitudes of an obtuse triangle. 80. Using constructions divide a given segment into a ratio of 3:2.ivide a seg into 5 = parts 81. onstruct a segment that is the geometric mean between segments and.

18 IRLES 82. The radius of a sphere is 25. plane intersects the sphere in a circle whose radius is 24. What is the distance between the center of the sphere and the plane? x = raw 2 circles so that the number of common tangents is 1. Internally tangent circles 84. Tangents PX & PY are drawn to circle O from point P. If PO = 12 and XPY is a right angle what is the length of the diameter? Explain. d = 12 2

19 85. Given: E ; is tangent to the circle at E Find the measure of each and give a reason or explanation. a. 1 x = 30 b. 5 x = 30 c. = x = 60 d. 2 x = 70 e. 3 x = 30 f. 4 x = 50 g. 6 x = 80 h. x = 50 i. E x = 100 j. Name 2 similar triangles. Triangle E and Triangle

### 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

### 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

### 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

### 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:

### 1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

### 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.

### 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

### 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

### 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:

### 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

### 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

### /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

### 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

### 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

### 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

### 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

### 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

### 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

### 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,

### 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

### 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,

### 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.

### 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

### Estimating Angle Measures

1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

### 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

### 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

### 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

### 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

### 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?

### 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

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 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 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

### 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

### Geometry 8-1 Angles of Polygons

. Sum of Measures of Interior ngles Geometry 8-1 ngles of Polygons 1. Interior angles - The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.

### 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

### 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,

### Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)

Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement

### 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 Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

### 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

### 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

### GEOMETRIC FIGURES, AREAS, AND VOLUMES

HPTER GEOMETRI FIGURES, RES, N VOLUMES carpenter is building a deck on the back of a house. s he works, he follows a plan that he made in the form of a drawing or blueprint. His blueprint is a model of

### A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

### 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

### 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

### 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

### 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

### 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

### Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures

SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]

### CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:

GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships

### 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

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### ACT Math Vocabulary. Altitude The height of a triangle that makes a 90-degree angle with the base of the triangle. Altitude

ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height

### 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

### Lesson 9.1 The Theorem of Pythagoras

Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius

### Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents

Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.

### 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

### 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

### 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

### QUADRILATERALS CHAPTER 8. (A) Main Concepts and Results

CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of

### Pythagorean Theorem: 9. x 2 2

Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

### Advanced Euclidean Geometry

dvanced Euclidean Geometry What is the center of a triangle? ut what if the triangle is not equilateral?? Circumcenter Equally far from the vertices? P P Points are on the perpendicular bisector of a line

### 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

### 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

### Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

### Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

### 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

### 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

### GEOMETRY COMMON CORE STANDARDS

1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

### GEOMETRY. Constructions OBJECTIVE #: G.CO.12

GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic

### " 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)

### Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test

Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan

### 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

### The Triangle and its Properties

THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter 6 6.1 INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three

### Target To know the properties of a rectangle

Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

### 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

### 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

### Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain

AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent

### 2, 3 1, 3 3, 2 3, 2. 3 Exploring Geometry Construction: Copy &: Bisect Segments & Angles Measure & Classify Angles, Describe Angle Pair Relationship

Geometry Honors Semester McDougal 014-015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 1-1 MAFS.91.G-CO.1.1 1 Use Segments & Congruence, Use Midpoint & 1-/1- MAFS.91.G-CO.1.1,

### Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons

CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining

### 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

### Geometry Made Easy Handbook Common Core Standards Edition

Geometry Made Easy Handbook ommon ore Standards Edition y: Mary nn asey. S. Mathematics, M. S. Education 2015 Topical Review ook ompany, Inc. ll rights reserved. P. O. ox 328 Onsted, MI. 49265-0328 This

### 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

### Contents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...

Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................

### 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.

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

### 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

### Unit 10 Geometry Circles. NAME Period

Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference

### How to fold simple shapes from A4 paper

How to fold simple shapes from 4 paper ndrew Jobbings www.arbelos.co.uk 18 February 2012 ontents Introduction 1 Square 2 Equilateral triangle 3 Rhombus 5 Regular hexagon 6 Kite 7 Why do the methods work?

### Geometry Unit 10 Notes Circles. Syllabus Objective: 10.1 - The student will differentiate among the terms relating to a circle.

Geometry Unit 0 Notes ircles Syllabus Objective: 0. - The student will differentiate among the terms relating to a circle. ircle the set of all points in a plane that are equidistant from a given point,

### 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)

### Duplicating Segments and Angles

CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty

### 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

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

### 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

### 43 Perimeter and Area

43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study

### Additional Topics in Math

Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications