This document discusses different ways to prove triangles are congruent using congruence postulates. It introduces the Side-Side-Side (SSS) postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. It also introduces the Side-Angle-Side (SAS) postulate, which states that if two sides and the included angle of one triangle are congruent to those of another triangle, then the triangles are congruent. Examples are provided to demonstrate using each postulate to prove triangles congruent. The document asks readers to practice identifying which postulate could be used to prove triangles congruent in different scenarios.

1. Proving Triangles are
Congruent
SSS and SAS Congruence
Postulates

2. ∠A P≅ ∠
∠B Q≅ ∠
∠C R≅ ∠
Corresponding AnglesCorresponding Sides
PQAB ≅
QRBC ≅
PRAC ≅
∆ABC ∆≅ PQR

3. Do we need to use all six pairs
to prove two triangles are
congruent?
Proving Triangles are
Congruent

4. SSS (Side-Side-Side) Congruence
Postulate
• If three sides of one triangle are congruent to
three sides of a second triangle, the two
triangles are congruent.
If Side PQAB ≅
QRBC ≅
PRAC ≅
∆ABC ∆≅ PQR
Then
Side
Side

5. Example 1
Prove: ∆DEF ∆≅ JKL
From the diagram,
.,, KLEFandJLDFJKDE ≅≅≅
SSS Congruence Postulate.∆DEF ∆≅ JKL

6. • If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of a second triangle, then the
two triangles are congruent.
SAS (Side-Angle-Side)
Congruence Postulate

7. Example 2
Prove: ∆SYT ∆≅ WYX

8. Which Congruence Postulate to
Use?
1. Decide whether enough information is
given in the diagram to prove that
triangle PQR is congruent to triangle
PQS. If so give a two-column proof and
state the congruence postulate.

9. Checkpoint
Decide if enough information is given to prove the
triangles are congruent. If so, state the
congruence postulate you would use.

10. Congruent Triangles in the
Coordinate Plane
Use the SSS
Congruence Postulate
to show that
∆ABC ∆≅ DEF
Which other
postulate could you
use to prove the
triangles are
congruent?

11. Closure Question

12. Homework
• Exercise 4.3 page 216: 1-19,
20, 21-27, 33, 35 odd.