Geometry
Triangle Congruence Day 4 Proving Congruence
Name_________________________
Date ______________
WARM UP
1. What do the reflexive, symmetric, and transitive properties say?
2. What’s the definition of (not the formula) of a midpoint?
3. If two segments or angles are congruent, what do you know about their actual numerical
values?
4. What does an angle bisector do?
5. What does a segment bisector do?
6. What do you know about complementary angles?
7. What do you know about supplementary angles?
8. What do you know about a linear pair?
9. Draw and label a set of vertical angles.
10. What are the five ways to prove triangles congruent?
STOP (and wait to review)
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 –
two column proof –
CPCTC –
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.
Example 4
Given: marked in diagram
JM  LM
Prove:
Statements
Reasons
1.
1. given
2.
2. given
3.
3. definition of a right angle
4. KMJ is a right angle
4.
5.
5. reflexive property
6. JKM  LKM
6.
7. JM  LM
7.
E
Example 5
Given:
BC  EC
AB  AD
DE  AD
Prove:
ABC  DEC
A
C
B
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
D