Geometry Mixed Practice Answer Key

Geometry/Trig 2 Name: __________________________ Unit 2 Mixed Practice – Answer Key Date: ___________________________ #1-2 Decide whether the given conditional is true or false. If it is false provide a counterexample to support your claim. Identify the hypothesis and conclusion of the conditional. Write the converse of the conditional. Decide whether the converse is true or false. If it is false provide a counterexample to support your claim. 1. If m1 = 120, then 1 is an obtuse angle. Conditional, True or False? True If false, provide a counterexample. N/A Hypothesis: m1 = 120 Conclusion: 1 is an obtuse angle Converse: If 1 is an obtuse angle, then m1 = 120. Converse, True or False? False If false, provide a counterexample. m1 = 100 (there are many possible answers). 2. If I live in the United States, then I live in Pennsylvania. Conditional, True or False? False If false, provide a counterexample. I live in New York. Hypothesis: I live in the United States. Conclusion: I live in Pennsylvania. Converse: If I live in Pennsylvania, then I live in the United States. Converse, True or False? True If false, provide a counterexample. N/A 3. Fill in the blanks. Given: MA = TH Prove: MT = AH M A Statements T Reasons 1. MA = TH 1. Given 2. MA + AT = TH + AT 2. Addition Property 3. MA + AT = MT 3. Segment Addition Postulate AT + TH = AH 4. MT = AH 4. Substitution H Geometry/Trig 2 Name: __________________________ Unit 2 Mixed Practice – Answer Key Date: ___________________________ T 4. Fill in the missing pieces of the proof. Given: TI = RG R I G Prove: TR = IG Statements Reasons 1. TI = RG 1. Given 2. TR + RI = TI 2. Segment Addition Postulate RI + IG = RG 3. TR + RI = RI + IG 3. Substitution 4. TR = IG 4. Subtraction 5. Match the statement with its corresponding reason. Statements: G_1. If M is the midpoint of DF, then DM = MF. B_2. If M is the midpoint of DF, then DM = ½DF. H_3. If BX is an angle bisector of ABC, then mABX = mXBC. C_4. If BX is an angle bisector of ABC, then mABX = ½mABC D_5. DM + MF = DF. A E_6. mABX + mXBC = mABC. X Reasons: A. Segment bisector theorem B. Midpoint theorem C B C. Angle bisector theorem D. Segment addition postulate E. Angle addition postulate F. Definition of a segment bisector G. Definition of a midpoint H. Definition of an angle bisector. D M F Geometry/Trig 2 Name: __________________________ Unit 2 Mixed Practice – Answer Key Date: ___________________________ Section 6 – State the postulate, definition, property, or theorem that allows you to draw each conclusion. L N 3 K M 2 1 P J 1. 2 @ 1. Vertical Angles are Congruent OR Vertical Angle Theorem. 2. If LMP is a right angle, then mLMP = 90. Definition of a right angle. 3. If 3 and 2 are complementary, then m2 + m3 = 90. Definition of Complementary Angles. 4. mKMN + mNMP = 180. Angle Addition Postulate 5. If m1 = m2 and m2 = m3, then m1 = m3. Substitution OR Transitive 6. If mJML + mNMP = 180, then JML and NMP are supplementary. Definition of Supplementary Angles. 7. KM + MP = KP Segment Addition Postulate 8. If M is the midpoint of JN, then JM = MN. Definition of a Midpoint 9. If MN bisects LMP, then m3 = ½mLMP. Angle Bisector Theorem 10. mJMK + mKMN = 180. Angle Addition Postulate 11. mJMK + mKML = mJML. Angle Addition Postulate 12. If mKMP = 180, then KMP is a straight angle. Definition of a Straight Angle Geometry/Trig 2 Name: __________________________ Unit 2 Mixed Practice – Answer Key Date: ___________________________ 7. Given: 1 x  3y  17; y  4 2 Prove: x = 10 Statements Reasons 1. ½x + 3y = 17; y = 4 1. Given 2. ½x + 12 = 17 2. Substitution 3. ½x = 5 3. Subtraction 4. x = 10 4. Multiplication 8. Given: m4 + m6 = 180 Prove: m5 = m6 4 5 Statements 6 Reasons 1. m4 + m6 = 180 1. Given 2. m4 + m5 = 180 2. Angle Addition Postulate 3. m4 + m5 = m4 + m6 3. Substitution 4. m4 = m4 4. Reflexive 5. m5 = m6 5. Subtraction