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.
Top Related