Geometry Chapter 2 Practice Free Response Test
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1 Geometry Chapter 2 Practice Free Response Test Directions: Read each question carefully. Show ALL work. No work, No credit. This is a closed note and book test.. Identify Hypothesis and Conclusion of the following statement. If two angles are supplementary, then their sum equals 80 degrees. Hypothesis: () Conclusion: () 2- Write a converse of each statement and determine if it is true or false. 2. If two segments are congruent, then their lengths are equal. Converse: (2) True or False: (). If a figure is a triangle, then it has three sides. Converse: (2) True or False: () 4. Write the following definition as a biconditional. A straight angle measures 80 degrees. Biconditional: (4) 5. Write a converse, inverse and contrapositive for the statement: If a figure is a hexagon, then it has six sides. a) Inverse: (2) b) Converse: (2) c) Contrapositive: (2)
2 Geometry Chapter 2 Practice Free Response Test 6-8 Determine if a valid conclusion can be reached from two true statements. If a valid conclusion is possible, state is and the law that was used. If a valid conclusion does not follow, write no conclusion. 6. a) If you spend money on it, then it s a business. b) If you spend money on it, then it is fun. Conclusion: (2) Law of (2) 7. a) If an angle is obtuse, then its measure is greater than 90 degrees. b) Angle 2 is obtuse. Conclusion: (2) Law of (2) 8. a) If two angles are vertical, then they are congruent. a. If two angles are congruent, then their measures are equal. Conclusion: (2) Law of (2) 9. Explain why this is or is not a good definition. (2) A segment is part of a line. 0. Find the measures of two complementary angles, Aand B, if m A= 7x+ 4 and m B= 4x+9. x= (2) <A= (2) <B= (2)
3 Geometry Chapter 2 Practice Free Response Test. Fill in the reason for each step. Given: 2x 7= x 2 Prove: x = Statement Reason. (2). 2x 7= x 2 2. (2) 2. (2x 7) = ( x 2). 6x 2= x 6. (2) 4. 5x 2= 6 4. (2) 5. 5x = 5 5. (2) 6. x = 6. (2) 2-6 Name the property that justifies each statement. 2. If UV = KL and KL = 6, thenuv = 6 2. (2). If m + m 2 = m 4 + m 2, then m = m 4. (2) 4. ABC ABC 4. (2) 5. (2) 5. If m D= 45, thenm D= If DEF HJK, then HJK DEF 6. (2)
4 Geometry Chapter 2 Practice Free Response Test 7-2 True or False. Write you answer clearly. Answers marked unclearly will be counted as wrong. 7. All right angles are congruent. 7. (2) 8. Two angles that form a right angle are 8. (2) complimentary. 9. Two angles that are supplementary are always 9. (2) congruent. 20. Two angles that supplementary are also 20. (2) complementary. 2. Vertical angles are always congruent. 2. (2) 22. A conclusion is a part of a conditional following IF 22. (2) 2. A biconditional statement is a combination of a conditional and its inverse. 2. (2) Complete each sentence with sometimes, always, or never. 24. Two angles that are supplementary form a linear pair. 25. Two angles that are congruent are right. 26. An angle is congruent to itself. 27. Vertical angles are adjacent. 28. Adjacent angles are congruent. 24. (2) 25. (2) 26. (2) 27. (2) 28. (2)
5 Geometry Chapter 2 Practice Free Response Test - ANSWERS Directions: Read each question carefully. Show ALL work. No work, No credit. This is a closed note and book test.. Identify Hypothesis and Conclusion of the following statement. If two angles are supplementary, then their sum equals 80 degrees. Hypothesis: two angles are supplementary () Conclusion: their sum equals 80 degrees () 2- Write a converse of each statement and determine if it is true or false. 2. If two segments are congruent, then their lengths are equal. Converse: If two segments lengths are equal, then they are congruent. (2) True or False: true (). If a figure is a triangle, then it has three sides. Converse: If a figure has three sides, then it is a triangle. (2) True or False: true () 4. Write the following definition as a biconditional. A straight angle measures 80 degrees. Biconditional An angle is straight if and only if it is 80 degrees. (4) 5. Write a converse, inverse and contrapositive for the statement: If a figure is a hexagon, then it has six sides. a) Inverse: If a figure is not a hexagon, then it does not have six sides. (2) b) Converse: If a figure has six sides, then it is a hexagon. (2) c) Contrapositive: If a figure does not have six sides, then it is not a hexagon (2)
6 Geometry Chapter 2 Practice Free Response Test - ANSWERS 6-8 Determine if a valid conclusion can be reached from two true statements. If a valid conclusion is possible, state is and the law that was used. If a valid conclusion does not follow, write no conclusion. 6. a) If you spend money on it, then it s a business. b) If you spend money on it, then it is fun. Conclusion: no conclusion possible (2) Law of (2) 7. a) If an angle is obtuse, then its measure is greater than 90 degrees. b) Angle 2 is obtuse. Conclusion:_Angle 2 has a measure greater than 90 degrees _(2) Law of Syllogism (2) 8. a) If two angles are vertical, then they are congruent. b) If two angles are congruent, then their measures are equal. Conclusion: If two angles are vertical then their measures are equal (2) Law of Syllogism (2) 9. Explain why this is or is not a good definition. (2) A segment is part of a line. This is not a good definition because a part of a line could also be a ray. 0. Find the measures of two complementary angles, Aand B, if m A= 7x+ 4 and m B= 4x+9. 7x+ 4+ 4x+ 9= 90 x= 7 (2) x + = 90 <A= 5 (2) x = 77 x = 7 <B= 7 (2)
7 Geometry Chapter 2 Practice Free Response Test - ANSWERS. Fill in the reason for each step. Given: 2x 7= x 2 Prove: x = Statement Reason. Given (2). 2x 7= x 2 2. Multiplication Property (2) 2. (2x 7) = ( x 2). 6x 2= x 6. Distributive Property 2) 4. 5x 2= 6 4. Subtraction Property (2) 5. 5x = 5 5. Addition Property (2) 6. x = 6. Division Property (2) 2-6 Name the property that justifies each statement. 2. If UV = KL and KL = 6, thenuv = 6 2. Substitution Property (2). If m + m 2 = m 4 + m 2, then m = m 4. Subtraction Property (2) 4. ABC ABC 4. Reflexive Property (2) 5. Multiplication Property (2) 5. If m D= 45, thenm D= If DEF HJK, then HJK DEF 6. Symmetric Property (2)
8 Geometry Chapter 2 Practice Free Response Test - ANSWERS 7-2 True or False. Write you answer clearly. Answers marked unclearly will be counted as wrong. 7. All right angles are congruent. 7. true (2) 8. Two angles that form a right angle are 8 true (2) complimentary. 9. Two angles that are supplementary are always 9. false (2) congruent. 20. Two angles that supplementary are also 20 false (2) complementary. 2. Vertical angles are always congruent. 2 true (2) 22. A conclusion is a part of a conditional following IF 22 false (2) 2. A biconditional statement is a combination of a conditional and its inverse. 2 false (2) Complete each sentence with sometimes, always, or never. 24. Two angles that are supplementary form a linear pair. 25. Two angles that are congruent are right. 26. An angle is congruent to itself. 27. Vertical angles are adjacent. 28. Adjacent angles are congruent. 24. sometimes (2) 25. sometimes (2) 26. always (2) 27. never (2) 28. sometimes (2)
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