Do Now: ≅ 𝐽𝐾 65° 115° 115°

Lesson 4-1: Congruent Figures Goal: Identify congruent figures and their corresponding parts.

Key Words: Corresponding parts (of congruent figures): The corresponding sides and angles in congruent figures. Congruent (figures): Two geometric figures that have exactly the same size and shape. When two figures are congruent, all pairs of corresponding angles and corresponding sides are congruent.

Example 1: List Corresponding Parts Given that ∆𝑷𝑴𝑵≅∆𝑬𝑫𝑪 , list all corresponding congruent parts. Corresponding Angles ∠𝑃≅∠𝐸 ∠𝑀≅∠𝐷 ∠𝑁≅∠𝐶 Corresponding Sides ∠𝑃𝑀≅∠𝐸𝐷 ∠𝑀𝑁≅∠𝐷𝐶 ∠𝑁𝑃≅∠𝐶𝐸

Example 2: Write a Congruence Statement The two triangles below are congruent. Identify all corresponding parts. ∠𝑲≅∠𝑸, ∠𝑯≅∠𝑷, ∠𝑱≅𝑹, 𝑲𝑱 ≅ 𝑸𝑹 , 𝑯𝑲 ≅ 𝑷𝑸 , 𝑯𝑱 ≅ 𝑷𝑹 Write a congruence statement. ∆𝑲𝑯𝑱≅∆𝑸𝑷𝑹

Example 3: Use properties of Congruent Triangles In this figure, ∆𝑺𝑻𝑼≅∆𝑾𝑿𝒀. Find the length of 𝑾𝑿 . Find 𝒎∠𝑺. 110° 8

Name corresponding Parts and congruent triangles ∠𝑆≅∠𝑌, ∠𝑈≅∠𝑍, ∠𝑇≅∠𝑋 28° 𝑆𝑇 ≅ 𝑌𝑋 , 𝑈𝑆 ≅ 𝑍𝑌 , 𝑇𝑈 ≅ 𝑋𝑍 3

Example 4: Determine whether triangles are congruent ∆𝐷𝐸𝐹≅∆𝐺𝐸𝐹

Example 5: Determine whether Triangles are congruent

Checkpoint: yes no yes no ∠𝐹 ∠𝑍 𝐸𝐷 𝑌𝑍

Checkpoint: 105° 45° 11.6 8.5 ∆𝐸𝐹𝐺≅∆𝐾𝐿𝐽

Assignment: P 222 – 223 #’s 8 – 44 even.