Objectives:- Explore triangle rigidity- Develop three congruence postulates

4.2 Triangle Congruence

Warm-Up:Triangles QRS and FDE are congruent. Write all pairs of corresponding parts.

D

E

F

Q

R

S

If you use the Polygon Congruence Postulate to show that two triangles are congruent, you must show that three pairs of sides are congruent and three pairs of angles are congruent. The following triangle postulates allow you to determine triangle congruence from limited information.

Note:

D

A

B

C

If the sides of one triangle are congruent to the sides of another triangle, then the two triangles are congruent.

SSS (Side-Side-Side) Postulate:

http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

SAS (Side-Angle-Side) Postulate:

If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.

ASA (Angle-Side-Angle) Postulate:

Example: The triangles below are congruent. Tell which congruent postulate allows you to conclude that they are congruent, based on the markings in the figures.

Example: The triangles below are congruent. Tell which congruent postulate allows you to conclude that they are congruent, based on the markings in the figures.

Example: The triangles below are congruent. Tell which congruent postulate allows you to conclude that they are congruent, based on the markings in the figures.

Example: Which triangle congruence postulate allows you to state that the following triangles are congruent?

D

A

B

C

Example: Determine whether each pair of triangles can be proven congruent by using the SSS, SAS, and ASA Congruence Postulate. If so write a congruence statement and identify which postulate is used.

A

B C

E

D

F

Example: Determine whether each pair of triangles can be proven congruent by using the SSS, SAS, and ASA Congruence Postulate. If so write a congruence statement and identify which postulate is used.

A B

C

D E

Example: Determine whether each pair of triangles can be proven congruent by using the SSS, SAS, and ASA Congruence Postulate. If so write a congruence statement and identify which postulate is used.

A

B C

D

Example: Some triangle measurements are given. Is there exactly one triangle that can be constructed with the given measurements? If so identify the postulate that justifies the answer.

∆ABC; m<A= AB=8, and AC=10

Example: Some triangle measurements are given. Is there exactly one triangle that can be constructed with the given measurements? If so identify the postulate that justifies the answer.

∆FGH; m<G= m<F, and GF=12

Example: Some triangle measurements are given. Is there exactly one triangle that can be constructed with the given measurements? If so identify the postulate that justifies the answer.

∆JKL; JK=5 LJ=7, and KL=5

Example: Some triangle measurements are given. Is there exactly one triangle that can be constructed with the given measurements? If so identify the postulate that justifies the answer.

∆XYZ; m<Y= m<X, and m<Z

Collins Writing Type 1:What is the advantage of using the SSS, SAS, & ASA Triangle Congruence Postulates instead of the Polygon Congruence Postulate given in lesson 4.1?

Homework:

Page 221; Numbers 5-19