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Transcript
Geometry Notes 4.6 Isosceles, Equilateral and Right Triangles Name: Hour: Lesson Goal: By the end of this lesson, you will be able to: Use properties of isosceles and equilateral triangles to show angle measures, side lengths, and prove triangle congruence. Use properties of right triangles to show angle measures, side lengths, and prove triangle congruence. - Prove triangle congruence using the Hypotenuse-Leg (HL) Theorem. - - Draw and label an ISOSCELES triangle with the following: Vertices A, B & C Legs Base Base Angles Vertex Angles BASE ANGLES THEOREM: If of a triangle are the opposite them are CONVERSE OF THE BASE ANGLES THEOREM: If are , then . of a triangle , then the opposite them are . Both of these statements are TRUE, so we can write this in the form of a statement! THEOREM: Two of a triangle are opposite them are if and only if the . Example 1: Use the diagram of ∆ABC to prove the Base Angles Theorem. ̅̅̅̅ ≅ 𝐴𝐶 ̅̅̅̅ GIVEN: In ∆ABC, 𝐴𝐵 ̅̅̅̅ is the bisector of BAC 𝐴𝐷 PROVE: B ≅ C An Statements 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. triangle is a special type of an isosceles triangle. If a triangle is EQUIANGULAR, then it is . If a triangle is EQUILATERAL, then it is . Example 2: Find the value of x and y. y Reasons So far we have learned about four ways to prove that triangles are congruent. SSS ( ) Congruence Postulate SAS ( ) Congruence Postulate ASA ( ) Congruence Postulate AAS ( ) Congruence Postulate There is ONE MORE WAY to prove triangle congruence. This way is SPECIAL because it can only be used when working with triangles. HYPOTENUSE-LEG (HL) CONGRUENCE THEOREM: Let’s practice figuring out which congruence theorem we should use with some examples! Congruence Theorem: Congruence Theorem: Congruence Theorem: Congruence Theorem: Congruence Theorem: