Geometry
Introduction to Proofs Worksheet
Name _______________________________________
Complete each proof by choosing a reason for each statement.
1.
Given:
Prove:
bisects
3≅ 2
3≅
SRT;
1
Statements
1.
bisects
SRT;
3≅
1
1. ______
2.
1≅
2
2. ______
3.
3≅
2
3. ______
2.
Reasons_________________
Choose from these reasons:
a) Definition of bisector
b) Substitution Property
c) Given
Given: BD = AD
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
c) Segment Addition Postulate
For #3 – 7, choose reasons from the following list for each proof.
a) Substitution Property
e) Definition of bisector
b) Angle Addition Property
f) Given
c) Definition of midpoint
g) Segment Addition Postulate
3.
Given:
Prove:
is the bisector of
2≅ 3
GAI;
Statements
1.
is the bisector of
1≅
3
Reasons
GAI;
1≅
3
1. __________________________________
2.
1≅
2
2. __________________________________
3.
2≅
3
3. __________________________________
.
4.
Given: AB = 9; BC = 7
Prove: 16 = AC
Statements
Reasons_________________
1. AB = 9; BC = 7
1. __________________________________
2. AB + BC = AC
2. __________________________________
3. 9 + 7 = AC
3. __________________________________
4. 16 = AC
4. __________________________________
5.
Given:
Prove:
≅
M is the midpoint of
≅
Statements
1.
2.
≅
Reasons_________________
; M is the midpoint of
1. __________________________________
≅
2. __________________________________
3.
≅
6.
Given: H is the midpoint of
Prove:
≅
3. __________________________________
Statements
1. H is the midpoint of
;
≅
Reasons_________________
;
≅
1. __________________________________
2.
≅
2. __________________________________
3.
≅
3. __________________________________
7.
Given:
Prove:
bisects
≅
;
≅
Statements
;
Reasons_________________
≅
1.
bisects
1. __________________________________
2.
≅
2. __________________________________
3.
≅
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
10.
11.
.
≅
MLP and
PLQ are adjacent angles.
12. LP is greater than MN.
13.
RMN and
14.
NLQ ≅
NMP form a linear pair.
NMP
15. M is between L and N.
16.
RML and
17.
NQL is a right angle.
18.
bisects
19.
intersects
NMP are vertical angles.
MLQ.
20. LM is less than LN.
21. m
MPQ is greater than m
MPL.
Use for #8-21.