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Download THEOREM 4-3 – Isosceles Triangle Theorem THEOREM 4
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Transcript
Advanced Geometry Topic 4 – Congruent Triangles NOTES – Isosceles & Equilateral Triangles (4-5) Name: _____________________________________________________ Date: _________________________________ Period: ____________ THEOREM 4-3 – Isosceles Triangle Theorem Theorem If… Then… __________ ≅ __________ If two ____________________ of a triangle are __________ ≅ __________ congruent, then the angles ____________________ those sides are ____________________. THEOREM 4-4 – Converse of the Isosceles Triangle Theorem Theorem If… Then… __________ ≅ __________ If two ____________________ of a triangle are __________ ≅ __________ congruent, then the sides ____________________ those angles are ____________________. THEOREM 4-5 Theorem If a line ____________________ the vertex angle of If… Then… __________ ≅ __________ and __________ ⊥ __________ and __________ ≅ __________ __________ ≅ __________ an isosceles triangle, then the line is also the ____________________ ____________________ of the base. Corollary to THEOREM 4-3 Corollary If a triangle is __________________________, then it If… Then… ________ ≅ ________ ≅ ________ ________ ≅ ________ ≅ ________ If… Then… ________ ≅ ________ ≅ ________ ________ ≅ ________ ≅ ________ is also __________________________. Corollary to THEOREM 4-4 Corollary If a triangle is __________________________, then it is also __________________________. (from the textbook) Proving the Isosceles Triangle Theorem Given: ̅̅̅̅ 𝑋𝑌 ≅ ̅̅̅̅ 𝑋𝑍 , ̅̅̅̅ 𝑋𝐵 bisects ∠𝑌𝑋𝑍 Prove: ∠𝑌 ≅ ∠𝑍 STATEMENTS REASONS ̅̅̅̅ ≅ ̅̅̅̅ 1) 𝑋𝑌 𝑋𝑍 2) Given 3) Definition of angular bisector 4) 5) ∆𝑋𝑌𝐵 ≅ ∆𝑋𝑍𝐵 6) Using the Isosceles Triangle Theorem and its Converse a. ̅̅̅? Explain. ̅̅̅̅ congruent to ̅𝑇𝑆 Is ∠𝑊𝑉𝑆 congruent to ∠𝑆? Is 𝑇𝑅 b. Can you conclude that ∆𝑅𝑈𝑉 is isosceles? Explain. (from the textbook) What is the value of 𝑥? Proving Triangles Congruent
