5.2 Congruent Polygons

What We Will Learn Identify and use corresponding parts Use Third Angles Thm.

Needed Vocab Corresponding parts: same location on different polygons

Ex. 1 Identifying Corresponding Parts Write congruence statement for the triangle and the corresponding parts When write statement, go in same direction and order Use corresponding parts to help with orientation △𝐽𝐾𝐿≅△𝑇𝑆𝑅 Order of congruency statement shows which corresponding parts are congruent Useful when no picture ∠𝐽≅∠𝑇; ∠𝐾≅∠𝑆; ∠𝐿≅∠𝑅 𝐽𝐾 ≅ 𝑇𝑆 ; 𝐽𝐿 ≅ 𝑇𝑅 ; 𝐾𝐿 ≅ 𝑆𝑅

Ex. 2 Using Congruent Polygons In the diagram, 𝐷𝐸𝐹𝐺≅𝑆𝑃𝑄𝑅 Orientation in congruency statement tells what is congruent to each other Find x 2𝑥−4=12 +4 +4 2𝑥=16 2𝑥 2 = 16 2 𝑥=8 6𝑦+𝑥=68 6𝑦+8=68 −8 −8 6𝑦=60 6𝑦 6 = 60 6 𝑦=10

Ex. 3/5 Proving Polygons Congruent Given: 𝑋𝑌 ∥ 𝑊𝑍 ; 𝑋𝑊 ∥ 𝑌𝑍 ; 𝑋𝑌 ≅ 𝑍𝑊 ; 𝑋𝑊 ≅ 𝑌𝑍 ; ∠𝑋≅∠𝑍 Prove: △𝑋𝑌𝑊≅ △𝑍𝑊𝑌 Statement Reason 1. 𝑋𝑌 ∥ 𝑊𝑍 ; 𝑋𝑊 ∥ 𝑌𝑍 ; 𝑋𝑌 ≅ 𝑍𝑊 ; 𝑋𝑊 ≅ 𝑌𝑍 ; ∠𝑋≅∠𝑍 1. Given 2. 𝑊𝑌 ≅ 𝑊𝑌 2. Reflex. Prop. 3. ∠𝑋𝑌𝑊≅∠𝑍𝑊𝑌; ∠𝑋𝑊𝑌≅∠𝑍𝑌𝑊 3. Alt. Int. Angles 4. △𝑋𝑌𝑊≅ △𝑍𝑊𝑌 4. Def of ≅ polygon

Ex. 4 Third Angle Thm. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Remember that all angles of a triangle add up to 180 degrees. Find 𝑚∠𝐵𝐷𝐶 Separate triangles and look at what given Find missing angle in triangle with given angle measurements Then use Third Angle theorem to find angle we want 𝑚∠𝐵𝐷𝐶=105