Geometry
Proving Triangles Congruent
Directions: Follow the proof. Label the diagram. Pick the reason to prove the
triangles congruent. Complete the congruence statement.
1. Given:
VW  XY
and
WX  YV
What other piece of information do you use to
Prove the triangles congruent? ______________
Reason triangles are congruent:
SAS, SSS, ASA, AAS, HL Theorem, or NEI
Congruence Statement:
VXY   ________
2. Given:
STN  SUH and SN  SH .
What other piece of information do you use to
Prove the triangles congruent? ______________
Reason triangles are congruent:
SAS, SSS, ASA, AAS, HL Theorem, or NEI
Congruence Statement:
SNT   ________
3. Given: QP  KJ and P is the midpoint of
KJ .
What other piece of information do you use to
Prove the triangles congruent? ______________
Reason triangles are congruent:
SAS, SSS, ASA, AAS, HL Theorem, or NEI
Congruence Statement:
QKP   ________
4. Given:
XQP is a right angle and CX  PX
What other piece of information do you use to
Prove the triangles congruent? ______________
Reason triangles are congruent:
SAS, SSS, ASA, AAS, HL Theorem, or NEI
Congruence Statement:
PQX   ________
5. Given: BAC  GCA
What TWO other piece of information do you use to
Prove the triangles congruent?
______________ & ________________
Reason triangles are congruent:
SAS, SSS, ASA, AAS, HL Theorem, or NEI
Congruence Statement:
CAG   ________
Tell which triangles you can show are congruent in order to prove the statement.
What postulate or theorem would you use?
1. BC  AD
4. BD  BE
2.
< TSU  < VSU
3. < ADB  < CBD
5. < KHN  < MGT
Use the diagram to write a “PLAN” for a proof.
6. PROVE: < DAB  < BCD
7. PROVE: ST  RQ
X
8. Proof Complete the proof.
GIVEN: YX  WX
X
ZX bisects < YXW.
PROVE: YZ  WZ
X
Statements
Reasons
1. YX  WX
2. ZX bisects < YXW.
1. __________________________________
2. __________________________________
3. < YXZ  < WXZ
3. __________________________________
4. XZ  XZ
5. YXZ   WXZ
4. __________________________________
6. YZ
 WZ
5. __________________________________
6. __________________________________
9. Proof Complete the proof.
GIVEN: AB ||CD , AB  CD
PROVE: ABC  DCB
Statements
Reasons
1. AB ||CD
2. <ABC  <DCB
1. ______________________________
2. ______________________________
3. AB  CD
3. ______________________________
4. CB  CB
4. ______________________________
5. ABC  DCB
5. ______________________________
10.
Proof Complete the proof.
GIVEN:WU ||YV , XU ||ZV , WX  YZ
PROVE: WXU  YZV
Statements
1. WU ||YV
2. UWX  VYZ
3. XU ||ZV
4. UXW  VZY
5. WX ||YZ
6. UWX  YZV
Reasons
1. __?__
2. __?__
3. __?__
4. __?__
5. __?__
6. __?__
Complete each proof.
1. Given: AB  CD
BC  DA
Prove: ABC  CDA
2.
Given : AB  CB ; EB  DB
Pr ove:
A
ABE  CBD
B
E
3.
C
D
Given:
ABC, ADC right
AB  AD
Prove: ABC  ADC
A
B
C
D
s
4.
5.
Given: A  C
BE  BD
Prove: ABE  CBD
A
C
B
E
D