1-7 intro to proof wksht

Geometry Worksheet
Introduction to Proof
Name:
Complete each proof by choosing a reason for each statement.
1.
Given: RV bisects <SRT; <3  <1
Prove: <3  <2
statements
.
1. RV bisects <SRT; <3  <1
1. ______
2. <1  <2
2. ______
3. <3  <2
3. ______
2.
reasons
.
Choose from these reasons:
a) Definition of bisector
b) Transitive Property
c) Given
Given: BD = AD and AD + DC = AC
Prove: BD + DC = AC
statements
.
1. BD = AD
1. ______
2. AD + DC = AC
2. ______
3. BD + DC = AC
3. ______
reasons
.
Choose from these reasons:
a) Substitution Property
b) Given
For #3 – 7, choose reasons from the following list for each proof.
a) Substitution Property
d) Definition of bisector
b) Given
e) Transitive Property
c) Definition of midpoint
3.
Given: AH is the bisector of <GAI, <1  <3
Prove: <2  <3
statements
.
reasons
1. AH is the bisector of <GAI, <1  <3
1. ______
2. <1  <2
2. ______
3. <2  <3
3. ______
.
(over)
4.
Given: AB = 9, BC = 7 and AB + BC = AC
Prove: 16 = AC
statements
.
1. AB = 9, BC = 7
1. ______
2. AB + BC = AC
2. ______
3. 9 + 7 = AC
3. ______
4. 16 = AC
4. ______
5.
reasons
.
reasons
.
reasons
.
Given: NA  AM
M is the midpoint of AB
Prove: NA  MB
statements
.
1. NA  AM ; M is the midpoint of AB
1. ______
2. AM  MB
2. ______
3. NA  MB
3. ______
6.
Given: H is the midpoint of GI , JH  HI
Prove: GH  JH
statements
.
1. H is the midpoint of GI , JH  HI
1. ______
2. GH  HI
2. ______
3. GH  JH
3. ______
7.
Given: TU bisects RS , UM  MS
Prove: RM  UM
statements
.
reasons
1. TU bisects RS , UM  MS
1. ______
2. RM  MS
2. ______
3. RM  UM
3. ______
.
For #8-21, indicate with yes or no whether or not the information can be assumed from the
diagram.
8. N, P, and Q are collinear.
9. M is the midpoint of LN .
10. NP  PQ
11. <MLP and <PLQ are adjacent angles.
12. LP is greater than MN.
13. <RMN and <NMP form a linear pair.
14. <NLQ  <NMP
15. M is between L and N.
16. <RML and <NMP are vertical angles.
17. <NQL is a right angle.
18. LP bisects <MLQ.
19. RP intersects LM
20. LM is less than LN.
21. m<MPQ is greater than m<MPL.
use for #8-21

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