8. C is the midpoint of BD. 4. AB < AE

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1 Assumptions and Justifications Use page 7 in your book to help complete the notes below Things You an Assume From a iagram Things You AN T Assume From a iagram I. For each picture list the facts you can assume from it. A T H L U N 1 8 W X U Y P L Q R N 1 2 II. Based on the picture alone, determine if each statement is true or false. 1. T SR 5. O O 2. S is a right angle. 6. OT TS. T is between and H. 7. O and R are collinear. 4., O, S, and H are coplanar. 8. TH is a right angle. O S H T R 1. AB is an acute angle. 6. B and B are supplementary. A 2. A B 7. AB and B are complementary.. AB B 8. is the midpoint of B. 4. AB < A 9. B and are a linear pair. 5. m B = AB and B are complementary. B

2 III. For each statement and its next logical conclusion, tell which definition, postulate, or theorem gives the justification. 1. Given: A WU A = WU 11. Given: R N 2. Given: is the midpoint of B B. Given: A bisects T A AT 4. Given: O = OL O OL 5. Given: AY and YAK are a linear pair. AY & YAK are supplementary 6. Given: TO is the supplement of SU m TO + m SU = Given: A and B lie in Plane JOG A and B are collinear 8. Given: A is in the interior of GL m GLA + m AL = m GL 9. Given: 1 is the complement to m 1 + m = Given: HA is vertical to HA AT AT U is the midpoint of RN 12. Given: 8 and 9 are vertical 1. Given: m NAT + m W = 90 NAT & W are complementary 14. Given: FA R FA = R 15. Given: A = TH A TH 16. Given: m AF + m BAT = 180 AF & BAT are supplementary 17. Given: R FRO ORG F 8 9 O G 18. Given: m 2 = m 6 2 6

3 Name: Period: aking onclusions 1. Given: TO AN 8. Given: I 7 K 5 2. Given: is the midpoint of B. Given: A bisects T 9. Given: F G F 4. Given: O = OL 10. Given: G 5. Given: AY and YAK are a linear pair 6. Given: TO is the supplement of SU 11. Given: m AB = m HIJ 12. Given: AT and RAP are vertical angles. 7. Given: 6 5 U T S 1. Given: SAT AT 14. Given: A is in the interior of GL

4 15. Given: FA R 21. Given: Given: HA is vertical to AT 22. Given: I L K 17. Given: R U N 18. Given; Given: PAI and IAR are a linear pair 24. Given: AT and angles. RAP are complementary 19. Given: m NAT + m W = Given: UB bisects RUY 25. Given: m NAT + m W = Given: A is between J and aking onclusions Worksheet continues on the next page

5 For #27 and 28, a two column proof is given but steps are missing. Fill in the missing steps and rewrite the whole proof correctly Given: 1 is supplementary to 2, is supplementary to 4, and 2 4 Prove: 1 Statements Reasons & 2 are supp. & 4 are supp. m 1 + m 2 = 180 m + m 4 = 180 Given ef. of Supplement.. m 1 + m 2 = m + m 4 Transitive Prop m 1 + m 4 = m + m 4 7. m 1 m 8. 1 Substitution prop, Steps and Subtraction prop. ef. of I K 5 Given: 5 is complementary to 7 Prove: I I Statements 1. 5 & 7 are comp. Reasons Given 2. m 5 + m 7 = 90 ef. of complement.. 4. m I = 90 Substitution, steps and 6. I I efinition of perpendicular

6 P 11 (4, 7, 8)

7 Name: Period: Proofs Worksheet #1 On a separate paper, write a two-column proof for each problem 1-5. Follow the plan provided for help. 1. Given: RT SU Prove: RS = TU R S T U Plan: Use the definition of congruent segments to write the given information in terms of lengths. Next use the Segment Addition Postulate to write RT in terms of RS + ST and SU as ST + TU. Substitute those into the given information and use the Subtraction Property of quality to eliminate ST and leave RS = TU. 2. Given: m 5 = 47 Prove: m 6 = U T S Plan: Use the Linear Pair Theorem to show that 5 and 6 are supplementary. Then use the definition of supplementary angles to show that their measures add up to 180. Finally use substitution and then subtraction to arrive at the Prove statement.. Given: AB = B B = B Prove: B is the midpoint of A A B Plan: Write the Given information and use the transitive property to show that AB=B. Then use the definition of congruence to show that the segments are congruent and the definition of midpoint to finish the proof. 4. Given: l bisects N at P Prove: P = PN P l Plan: Use the definition of bisect to show the two smaller segments are congruent. Then use the definition of congruence to show that their lengths are equal. N 5. Given: 1 and 2 are supplementary; 1 Prove: and 2 are supplementary 1 2 Plan: Use the definition of supplementary angles and congruent angles to write the given information in terms of angle measures. Next use substitution to show that m + m 2 = 180. Then use the definition of supplementary angles for the conclusion.

8 Proofs Worksheet #2 W 1. N O 2. A B Given: O is the midpoint of N O = OW Prove: OW = ON Given: AB = Prove: A = B. W B 4. A X U Y Given: m 1 = 90 Given: 1 and 2 are complementary Prove: m 2 = 90 and 2 are complementary Prove: m 1 = m 5. J K 6. W L O X U Y Given: m 1 = m Given: m 1 = 90 Prove: m JOL = m KO Prove: m = 180 P Q R L N G Given: PR LN Given: F G Q is the midpoint of PR is in the interior of FG is the midpoint of LN Prove: F and G are complementary Prove: PQ = L F A B 1 2 Given: AB Given: 1 and 2 are supplementary Prove: A B 1 2 Prove: 1 and 2 are right angles Given: 1 2 Given: 1 and 2 are complementary Prove: 1 and 2 are right angles Prove: 2 and are complementary