Geometry
Triangle Congruence - Day 5 - More Proofs
Name_______________________________
Warm-Up
State the third congruence that must be given to prove that PQR  STU using the indicated postulate or
theorem. (Hint: sketch the triangles first and mark the given information)
1. GIVEN:
Q  T, PQ  ST
Use the AAS Congruence Theorem
2. GIVEN:
R  U, PR  SU
Use the ASA Congruence Postulate
In the following figures determine if triangles the two triangles can be proven congruent by SSS, SAS, AAS,
HL, or ASA
3. ________
4. ________
5. _________
6. _________
What’s a valid proof “Reason?”
Givens
- “given”
- in diagram
Properties
- addition
- subtraction
- multiplication
- division
- substitution
- distribution
- reflexive
- symmetric
- transitive
Definition of…
- midpoint
- congruent segments
- congruent angles
- bisector (angle or
segment)
- complementary
angles
- supplementary
angles
- linear pair
- vertical angles
Other common reasons
- all right angles are
congruent
- angle addition postulate
- segment addition
postulate
- 5 ways to prove triangles
congruent
NEVER EVER USE: Proven!!!!
1. Write a complete proof by matching each statement with its corresponding reason.
Given:
QS is an angle bisector of PQR.
Prove:
mPQS 
P
S
1
mPQR
2
Q
R
_____
1. QS is an angle bisector of PQR.
A. Definition of angle bisector
_____
2. PQS  SQR
B. Combining like terms
_____
3. mPQS  mSQR
C. Angle addition postulate
_____
4. mPQS  mSQR  mPQR
D. Given
_____
5. mPQS  mPQS  m PQR
E. Division property of equality
_____
6. 2  mPQS  mPQR
F. Definition of congruent angles
_____
7. mPQS 
1
mPQR
2
G. Substitution property of equality
2.
Given:
AK  CJ, BJK  BKJ, A  C
Prove:
BK  BJ
Statements
Reasons
1. AK  CJ
1. Given
2.
2. Given
3.
3.
4. ABK  CBJ
4.
5.
5. CPCTC
3.
Given: VW  UW, X  Z
Prove: V  U
Statements
Reasons
1. VW  UW
1.
2.
2. Given
3.
3. Reflexive property
4.
4.
5. V  U
5.
4.
Given:
AC  BC
M is the midpoint of AB
Prove:
ACM  BCM
C
A
Statements
Reasons
1. AC  BC
1.
2.
2. Given
3. AM  BM
3.
4.
4. Reflexive property
5.
ACM  BCM
5.
M
B