Proving Triangles are Congruent

SSS and SAS Congruence Postulates

∠A P≅ ∠

∠B Q≅ ∠

∠C R≅ ∠

Corresponding AnglesCorresponding Sides

PQAB QRBC PRAC

∆ABC ∆≅ PQR

Do we need to use all six pairs to prove two triangles are congruent?

Proving Triangles are Congruent

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

Example 1

Prove: ∆DEF ∆≅ JKL

From the diagram,

.,, KLEFandJLDFJKDE

SSS Congruence Postulate.∆DEF ∆≅ JKL

• 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

Example 2

Prove: ∆SYT ∆≅ WYX

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.

CheckpointDecide if enough information is given to prove the

triangles are congruent. If so, state the congruence postulate you would use.

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?

Closure Question

Homework

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