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Download THEOREM 4-1 – Third Angles Theorem Finding Congruent Sides
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Geometry Topic 4 – Congruent Triangles NOTES – Congruent Figures (4-1) Definition Name: _____________________________________________________ Date: _________________________________ Period: ____________ Example Congruent polygons have congruent corresponding ________________ and ________________. When you name congruent polygons, you must list corresponding ________________ in the same order. THEOREM 4-1 – Third Angles Theorem Theorem If… Then… If two angles of one triangle are congruent to two angles of another triangle, then the ________________ angles are ________________. Finding Congruent Sides & Angles If ∆𝑊𝑌𝑆 ≅ ∆𝑀𝐾𝑉, what are the congruent corresponding parts? Using Congruent Sides & Angles Suppose that ∆𝑊𝑌𝑆 ≅ ∆𝑀𝐾𝑉. If 𝑚∠𝑊 = 62 and 𝑚∠𝑌 = 35, what is 𝑚∠𝑉? Explain. Finding Congruent Triangles Is ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷? Justify your answer. (from the textbook) Proving Triangles Congruent ̅̅̅̅, ̅̅̅̅̅ ̅̅̅̅ ≅ 𝐿𝑂 Given: 𝐿𝑀 𝑀𝑁 ≅ ̅̅̅̅ 𝑂𝑁 , ∠𝑀 ≅ ∠𝑂, ∠𝑀𝐿𝑁 ≅ ∠𝑂𝐿𝑁 Prove: ∆𝐿𝑀𝑁 ≅ ∆𝐿𝑂𝑁 STATEMENTS REASONS 1) ̅̅̅̅ 𝐿𝑀 ≅ ̅̅̅̅ 𝐿𝑂 , ̅̅̅̅̅ 𝑀𝑁 ≅ ̅̅̅̅ 𝑂𝑁 ̅̅̅̅ ≅ 𝐿𝑁 ̅̅̅̅ 2) 𝐿𝑁 3) ∠𝑀 ≅ ∠𝑂, ∠𝑀𝐿𝑁 ≅ ∠𝑂𝐿𝑁 4) ∠𝑀𝑁𝐿 ≅ ∠𝑂𝑁𝐿 5) ∆𝐿𝑀𝑁 ≅ ∆𝐿𝑂𝑁 Proving Triangles Congruent Given: ̅̅̅̅ 𝐴𝐸 ≅ ̅̅̅̅ 𝐷𝐶 , ̅̅̅̅ 𝐸𝐵 ≅ ̅̅̅̅ 𝐶𝐵, ̅̅̅̅ 𝐵𝐴 ≅ ̅̅̅̅ 𝐵𝐷 , ∠𝐴 ≅ ∠𝐷 Prove: ∆𝐴𝐸𝐵 ≅ ∆𝐷𝐶𝐵 STATEMENTS REASONS 1) ̅̅̅̅ 𝐴𝐸 ≅ ̅̅̅̅ 𝐷𝐶 , ̅̅̅̅ 𝐸𝐵 ≅ ̅̅̅̅ 𝐶𝐵 , ̅̅̅̅ 𝐵𝐴 ≅ ̅̅̅̅ 𝐵𝐷 2) Given 3) ∠𝐴𝐵𝐸 ≅ ∠𝐷𝐵𝐶 4) 5) Third Angles Theorem
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