Problem of the Day.

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Presentation transcript:

Problem of the Day

Summary

Section 4-5b HL and CPCTC

Then Now Objectives You proved triangles congruent using ASA and AAS. Use the HL Postulate to test for congruence. Prove sides and angles congruent using CPCTC.

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 3) Construct viable arguments and critique the reasoning of others. 5) Use appropriate tools strategically. Common Core State Standards

Hypotenuse-Leg Congruence

How are the triangles congruent?

C P T orresponding arts of ongruent riangles are REMEMBER!! CPCTC will NEVER be used in a proof BEFORE proving two triangles congruent!!

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

Given: 𝑁𝑃 ≅ 𝑃𝑀 ∠𝑁𝑃𝐿 and ∠𝑀𝑃𝐿 are rt. ∠𝑠 Prove: ∠𝑁≅∠𝑀 Example 3

Given: 𝐴𝐵 ≅ 𝐶𝐵 ∠A ≅ ∠C 𝐷𝐵 bisects ∠ABC Prove: 𝐴𝐷 ≅ 𝐷𝐶 Example 1

Given: S is the midpoint of 𝑄𝑇 𝑄𝑅 || 𝑇𝑈 Prove: 𝑄𝑅 ≅ 𝑇𝑈 Example 2

p.270 #14 p.279 #11, 12, 17 p.284 #9 (Write a two column proof for #14, 11, 12, and 17.) Homework