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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