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Geometry
Triangle Congruence Day 3 Proving Congruence
Name_________________________
Date ______________
Today, we will review how to use a two column proof to prove triangles and parts of
triangles are congruent
At the end of class, you will be able to complete/fill in proofs using congruence
theorems.
Proofs
proof – A logical argument that shows a ___________________ is ___________.
two column proof – has numbered ________________ and corresponding ___________________
that show an argument in a logical order.
CPCTC – ________________________ Parts of __________________ Triangles are Congruent.
Examples
1. Explain how you can prove that BAD  BCD.
B
A
C
D
N
2. Explain how you can prove that LK  PN .
M
L
K
P
Geometry Proving Congruence in Triangles (continued)
Now let’s organize our thoughts into a two column proof!
Example 3
Given:
X is the midpoint of VY
X is the midpoint of WZ
Prove:
VWX  YZX
Statements
Reasons
1. X is the midpoint of VY
1.
2. X is the midpoint of WZ
2.
3.
3. definition of a midpoint
4.
4. definition of a midpoint
5. VXW  YXZ
5.
6. VWX  YZX
6.
S
Example 4
P
Given:
PR  SQ
PQ  PS
Prove:
RS  RQ
Q
Statements
Reasons
1. PR  SQ
1.
2.
3. PR  PR
R
2. Given
3.
4.
4.
5.
5.
E
Example 5
Given:
Prove:
BC  EC
AB  AD
DE  AD
A
ABC  DEC
B
C
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
D