Proofs - Assumption and Justification



Proofs - Assumption and Justification

Things you Can assume from a diagram: Things you Cannot assume from a diagram:

For each picture, list what can you assume.

1) 2) 3) 3

1 2 A B C 4

4) 6 5) 6) 10

11

5 7

9 8

Based on the picture alone, determine if each statement is true or false.

7) (BCE & (EDC are a linear pair ______________

8) [pic] ______________

9) (ABE & (EBC are complementary ______________

10) (ABE ( (EBC ______________

11) m(EBC = 90 ______________

12) C is midpoint of [pic]______________

13) C is between B & D ______________

14) [pic]ll[pic] ______________

For each statement and its logical conclusion, tell which definition, postulate, theorem or property gives the justification.

15) Given: A is the midpoint of [pic] 16) Given: (1 is vertical to (2

Conclusion: [pic] Conclusion: (1 ( (2

____________________________________ __________________________________

17) Given: (3 is supplementary to (4 18) Given: MA = TH

Conclusion: m(3 + m(4 = 180 Conclusion: [pic]

____________________________________ ____________________________________

19) Given: [pic] is the angle bisector of (ABC 20) Given: [pic] and G,H, & J collinear

Conclusion: (ABD ( (DBC Conclusion: H is the midpoint of [pic]

______________________________________ _____________________________________

21) Given: (5 & (6 are a linear pair 22) Given: m(6 + m(7 = 90

Conclusion: (5 & (6 are supplementary Conclusion: (6 & (7 are complementary

______________________________________ _____________________________________

23) Given: m(8 = 90 24) Given:

Conclusion: (8 is a right angle A B C

Conclusion: AB + BC = AC

_____________________________________ _____________________________________

25) Given: m(1 = 90 & m(2 = 90 26) Given: (CDF ( (FDE

Conclusion: m(1 = m (2 Conclusion: m(CDF = m(FDE

_____________________________________ ____________________________________

27) Given: 28) Given: (ABD ( (DBC

H J K Conclusion: [pic] is the angle bisector of (ABC

Conclusion: J is the midpoint of [pic]

_____________________________________ _____________________________________

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M

F

D

E

A

D

C

B

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