3.2 Three Ways To Prove Triangles Congruent Objective: After studying this lesson you will be able to identify included angles and included sides as well as apply the SSS, SAS, ASA postulates.

In the figure at the right, H is included by the sides GH and HJ. Which sides include G? Which angles include HJ?

Triangles have some special properties to help us prove that 2 triangles are congruent using only 3 specially chosen pairs of corresponding parts. If you have three toothpicks (sides) of different lengths you can create a triangle. If your friend has three toothpicks (sides) that have the same measure as your toothpicks then your friend can create a triangle that is congruent to the one that you built.

B O W T I E Postulate If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent. (SSS)

B O W T I E Postulate If there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. (SAS)

B O W T I E Postulate If there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. (ASA)

Using the congruent markings determine what is needed to prove the triangles congruent using the specific methods. T T O M SSS SAS A C

T D A M O N SAS ASA

P R W V T S SAS ASA

Given: D Prove: A C B Statement Reason 1. 2. 3. 4. 5. 1. 2. 3. 4. 5.

Given: Prove: Reason Statement R 3 4 5 6 K M O P 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8. Given If 2 angles form a straight angle, they are supp. If 2 angles form a straight angle, they are supp. angles supp. to congruent angles are congruent Given Given Subtraction property ASA (steps 4, 5, 7)

Summary: How many parts are there in proving triangles congruent? What are the shortcuts that we can use to prove triangles congruent? Homework: worksheet