1. 5.2 Congruent Polygons

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

3. Needed Vocab
Corresponding parts: same location on different polygons

4. 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

5. 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
2𝑥=16
2𝑥 2 = 16 2
𝑥=8
6𝑦+𝑥=68
6𝑦+8=68
−8 −8
6𝑦=60
6𝑦 6 = 60 6
𝑦=10

6. 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

7. 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