Igor noticed on a map that the triangle whose vertices are the supermarket, the library, and the post office (△SLP) is congruent to the triangle whose vertices are Igor’s home, Jacob’s home, and Ben’s home (△IJB). That is, △SLP ≅ △IJB. The distance between the supermarket and the post office is 1 mile. Which path along △IJB is congruent to this? The measure of ∠LPS is 40. Identify the angle that is congruent to this angle in △IJB. Problem of the Day

Section 4-4a Proving Triangles Congruent - SSS

Then Now Objectives You proved triangles congruent using the definition of congruence. Use the SSS Postulate to test for triangle congruence.

Common Core State Standards Content Standards G.CO.10 – Prove theorems about triangles. G.SRT.5 – Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 1) Make sense of problems and persevere in solving them. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

You and your partner should have six straws, three of one color and three of another color. Pick a color and take those three straws. How are your three straws and your partner’s three straws similar? Make a triangle using your three straws. Are the two triangles you and your partner made congruent? CHALLENGE: Between you and your partner, try to make two triangles that are NOT congruent (you still have to use the same color of straws to create the triangle). Partner Activity

Side-Side-Side Congruence (SSS)

Q U Given: 𝑄𝑈 ≅ 𝐴𝐷 𝑄𝐷 ≅ 𝐴𝑈 Prove: ∆𝑄𝑈𝐴≅∆𝐴𝐷𝑄 Example 1 D A

Given: 𝑅𝑆 ≅ 𝑇𝑆 V is the midpoint of 𝑅𝑇 Prove: ∆𝑅𝑆𝑉≅∆𝑇𝑆𝑉 Example 1

Given: ∆QRS is isos. with 𝑄𝑅 ≅ 𝑆𝑅 𝑅𝑇 bisects 𝑄𝑆 at point T Prove: ∆𝑄𝑅𝑇≅∆𝑆𝑅𝑇 Example 1

p.269 #5, 6, 16, 21, 38, 39 (Write a two-column proof for #5, 6, and 21) Homework