Some Ways to Prove Triangles Congruent

Some Ways to Prove Triangles Congruent
Relative Positions of parts of a Triangle:
A
̅̅̅̅ is opposite ∠C
̅̅̅̅ is included between ∠A and ∠B.
∠A is opposite ̅̅̅̅
∠A is included between ̅̅̅̅ and ̅̅̅̅
B
C
In order for two triangles to be congruent, all 6 corresponding parts must be congruent.
However, if we needed to show that two triangles were congruent, we would NOT need to show
all 6 corresponding parts congruent. There are 5 ways of showing triangles congruent by only
knowing 3 specific corresponding parts.
We will look at 3 methods today:
1. SAS Postulate: If two sides and the included angle of 1 triangle are congruent to two
sides and the include angle of another triangle, then the triangles are congruent.
X
P
R
Q
Z
Y
2. SSS Postulate: If three sides in one triangle are congruent to 3 sides in another triangle,
then the triangles are congruent.
X
P
Q
R
Z
Y
3. ASA Postulate: If two angles and the included side of 1 triangle are congruent to two
angles and the include side of another triangle, then the triangles are congruent.
X
P
Z
R
Q
Y
Examples:
State if the following triangles are congruent and why:
1.
2.
Y
3. Proof:
̅̅̅̅
Given: ̅̅̅̅
̅̅̅̅ bisects ∠YBZ
Prove:
A
1
2
3
4
Z
Statement
Reason
B