1. Ways to Prove Triangles Congruent
Section 4-2
Ways to Prove Triangles Congruent

2. Side, Side, Side Postulate
(SSS Postulate)
If three sides of one triangle…
are congruent to three sides of another triangle,
then the triangles are congruent.

3. Example Do we have two congruent triangles here? A A P R
In this picture, there are only two sides marked congruent.
But the two triangles also share side AT. S
AP = AR given
PT = RT given
AT = AT reflexive prop
▲PAT  ▲RAT SSS Postulate S T T S

4. Side, Angle, Side Postulate
(SAS Postulate)
If two sides and the included angle of one triangle…
are congruent to two sides and the included angle of another triangle,
then the triangles are congruent.

5. Example Do we have two congruent triangles here? A C
In this picture, there are only two sides marked congruent. R 2 1
But the two triangles will have congruent angles (vertical angles) S H S
CR = SR given
HR = AR given
m<1 = m< vertical angles
▲CRH  ▲SRA SAS Postulate S A

6. Angle, Side, Angle Postulate
(ASA Postulate)
If two angles and the included side of one triangle…
are congruent to two angles and the included side of another triangle,
then the triangles are congruent.

7. Example A Given: AT = YT, and m<A = m<Y Prove: YP = AR
It would be easy to prove YP= AR if we had 2 congruent triangles P 2 1 T R
Statements
Reasons A
m<Y = m<A given
YT = AT given
m<1 = m< vertical angles
▲YTP  ▲ATR ASA Postulate
YP = AR CPCTC Y S A
Nice Job!!!

8. It’s all about choices…
The triangles must be congruent because there is only one way to create a triangle with those specifications
8 cm
38˚
6 cm
3 sides
An angle between 2 sides
67˚
32˚
A side between 2 angles

9. Think About This… 1 2 Are these triangles congruent?
Are the triangles congruent by ASA?
What can you conclude about <1 and <2?
<1  <2
Now are these triangles congruent by ASA?
Try classroom exercises – pg (1-9)