Name: Class: Date: ID: A Geometry Chapter 1-2 Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Based on the pattern, what is the next figure in the sequence? 4. Name an angle supplementary to COB. a. b. c. d. 2. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale. a. x = 8, ST = 24 b. x = 8, ST = 36 c. x = 3, ST = 24 d. x = 3, ST = 36 3. If m EOF = 20 and m FOG = 36, then what is the measure of EOG? The diagram is not to scale. a. 40 b. 16 c. 56 d. 72 a. AOE b. BOE c. COD d. BOA 5. Supplementary angles are two angles whose measures have the sum of. Complementary angles are two angles whose measures have the sum of. a. 180; 90 b. 90; 180 c. 90; 45 d. 180; 360 6. The complement of an angle is 36. What is the measure of the angle? a. 54 b. 144 c. 154 d. 64 7. Find the distance between points P(6, 4) and Q(5, 6) to the nearest tenth. a. 2.2 b. 5 c. 3 d. 14.9 1
Name: ID: A 8. Each unit on the map represents 1 mile. What is the actual distance from Oceanfront to Seaside? Round your answer to the nearest whole number. 11. Find the length of the missing side. The triangle is not drawn to scale. a. about 9 miles b. about 7 miles c. about 8 miles d. about 10 miles 9. Find the coordinates of the midpoint of the segment whose endpoints are H(9, 4) and K(7, 2). a. (16, 6) b. (1, 1) c. (2, 2) d. (8, 3) 10. M(7, 4) is the midpoint of RS. The coordinates of S are (9, 6). What are the coordinates of R? a. (5, 2) b. (11, 8) c. (8, 5) d. (14, 8) 12. a. 10 b. 9 c. 100 d. 12 Find the length of the missing side. Leave your answer in simplest radical form. a. 6 cm b. 218 cm c. 2 5 cm d. 2 30 cm 13. A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain. a. no; 8 2 + 19 2 14 2 b. no; 8 2 + 15 2 17 2 c. no; 8 2 + 19 2 = 14 2 d. yes; 8 2 + 15 2 = 17 2 2
Name: ID: A 14. Find a counterexample to show that the conjecture is false. Conjecture: Any number that is divisible by 5 is also divisible by 10. a. 32 b. 50 c. 40 d. 25 15. Identify the segment bisector of AB. Then find BM. a. line M; BM = 12 b. M; BM = 49 c. M; BM = 12 d. line M; BM = 49 16. Find the area of FGH with coordinates FÊ ËÁ 4,6 ˆ,G Ê Ë 2, 1 Ê ËÁ 2,6 ˆ. a. 7 square units b. 21 square units c. about 21.34 square units d. 42 square units 17. In the diagram, m BDA = 144. Find m ADC. 18. BDA is a straight angle. Find m BDC. a. 16 b. 112 c. 60 d. 68 19. The measure of an angle is nine times the measure of its complement. Find the measure of the larger angle. a. 80 b. 162 c. 160 d. 81 20. Find the values of x and y. a. x = 20, y = 2 b. x = 8, y = 14 c. x = 20, y = 14 d. x = 8, y = 2 a. 91 b. 82 c. 62 d. 40 3
Name: ID: A 21. Let p be you are a senior and let q be you are in high school. Write the converse. Then decide whether it is true or false. a. If you are a senior, then you are in high school; true b. If you are in high school, then you are a senior; false c. If you are not a senior, then you are not in high school; false d. If you are not in high school, then you are not a senior; true Short Answer 22. Complete the proof. Given AB = CD Prove AC = BD STATEMENTS REASONS 1. AB = CD 1. Given 2. BC = BC 2. 3. AB + BC = CD + BC 3. Addition Property of Equality 4. 4. Segment Addition Postulate 5. CD + BC = BD 5. Segment Addition Postulate 6. 6. Substitution Property of Equality 4
Name: ID: A Fill in each missing reason. 23. Given: m AOC = 150 m AOB + m BOC = m AOC 2x + 6(x 3) = 150 2x + 6x 18 = 150 8x 18 = 150 8x = 168 x = 21 a. b. c. d. e. f. Free Response 24. Use the given information to make a two column proof. 5
ID: A Geometry Chapter 1-2 Exam Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L2 REF: 1-1 Patterns and Inductive Reasoning OBJ: 1-1.1 Using Inductive Reasoning STA: CA GEOM 1.0 CA GEOM 3.0 TOP: 1-1 Example 1 KEY: pattern inductive reasoning 2. ANS: C PTS: 1 DIF: L2 REF: 1-5 Measuring Segments OBJ: 1-5.1 Finding Segment Lengths TOP: 1-5 Example 3 KEY: segment segment length midpoint multi-part question 3. ANS: C PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.1 Finding Angle Measures TOP: 1-6 Example 3 KEY: Angle Addition Postulate 4. ANS: B PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4 KEY: supplementary angles 5. ANS: A PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4 KEY: supplementary angles complementary angles 6. ANS: A PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4 KEY: complementary angles 7. ANS: A PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: 1-8.1 Finding Distance on the Coordinate Plane TOP: 1-8 Example 1 KEY: Distance Formula coordinate plane 8. ANS: C PTS: 1 DIF: L3 REF: 1-8 The Coordinate Plane OBJ: 1-8.1 Finding Distance on the Coordinate Plane KEY: coordinate plane Distance Formula word problem problem solving 9. ANS: D PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: 1-8.2 Finding the Midpoint of a Segment TOP: 1-8 Example 3 KEY: coordinate plane Midpoint Formula 10. ANS: A PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane OBJ: 1-8.2 Finding the Midpoint of a Segment TOP: 1-8 Example 4 KEY: coordinate plane Midpoint Formula 11. ANS: A PTS: 1 DIF: L1 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 TOP: 8-1 Example 1 KEY: Pythagorean Theorem leg hypotenuse MSC: NAEP G3d CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 12. ANS: D PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem STA: CA GEOM 15.0 TOP: 8-1 Example 2 KEY: Pythagorean Theorem leg hypotenuse 1
ID: A 13. ANS: D PTS: 1 DIF: L1 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.2 The Converse of the Pythagorean Theorem NAT: NAEP 2005 G3d ADP I.4.1 ADP J.1.6 ADP K.1.2 ADP K.5 ADP K.10.3 TOP: 8-1 Example 4 KEY: Pythagorean Theorem MSC: NAEP G3d CAT5.LV20.50 CAT5.LV20.55 CAT5.LV20.56 IT.LV16.AM IT.LV16.CP S9.TSK2.GM S9.TSK2.PRA S10.TSK2.GM S10.TSK2.PRA TV.LV20.13 TV.LV20.14 TV.LV20.52 14. ANS: D PTS: 1 DIF: L2 REF: 1-1 Patterns and Inductive Reasoning OBJ: 1-1.1 Using Inductive Reasoning STA: CA GEOM 1.0 CA GEOM 3.0 TOP: 1-1 Example 3 KEY: conjecture counterexample 15. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.3 NAT: HSG-GPE.B.7 KEY: segment bisector NOT: Example 2 16. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.4 NAT: HSG-GPE.B.7 HSG-MG.A.1 KEY: coordinate plane area NOT: Example 3 17. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.5 NAT: HSG-CO.A.1 KEY: measure of an angle angle NOT: Example 4 18. ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.5 NAT: HSG-CO.A.1 KEY: measure of an angle angle NOT: Example 4 19. ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.6 NAT: HSG-CO.A.1 KEY: complementary angles NOT: Example 5 20. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 2.6 NAT: HSG-CO.C.9 KEY: using angle relationships NOT: Example 4-2 21. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 2.1 NAT: HSG-CO.C.9 HSG-CO.C.10 HSG-CO.C.11 HSG-SRT.B.4 KEY: conditional statement converse inverse contrapositive application NOT: Example 3 SHORT ANSWER 22. ANS: Statement 4: AB + BC = AC, Statement 6: AC = BD, Reason 2: Reflexive Property of Equality PTS: 1 DIF: Level 1 REF: Geometry Sec. 2.5 NAT: HSG-CO.C.9 KEY: properties of equality NOT: Application-1 2
ID: A 23. ANS: a. Angle Addition Postulate b. Substitution Property c. Distributive Property d. Simplify e. Addition Property of Equality f. Division Property of Equality PTS: 1 DIF: L3 REF: 2-4 Reasoning in Algebra OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry STA: CA GEOM 1.0 CA GEOM 3.0 TOP: 2-4 Example 1 KEY: proof deductive reasoning Properties of Equality multi-part question OTHER 24. ANS: 461 mi; If the round-trip distance between City Y and City X is 126 miles, then the one-way distance is 63 miles. If the round-trip distance between City X to City Z is 796 miles, then the one-way distance is 398 miles. 63 + 398 = 461 PTS: 1 DIF: Level 3 REF: Geometry Sec. 1.2 NAT: HSG-CO.A.1 KEY: distance application NOT: Example 4 3