4.7 Use Isosceles and Equilateral Triangles

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Presentation transcript:

4.7 Use Isosceles and Equilateral Triangles

Define Isosceles A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles)

Isosceles Triangle vertex Leg Leg base angle base angle Base

Isosceles Triangle Theorem (Base Angles Theorem) If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent A B C

~ J K L Given: JK = JL Prove <K = <L ~ M S R 1. Define M as the midpoint of the base 1. Definition of a midpoint 2. Draw JM 2. Two points determines a line ~ 3. MK = ML 3. Definition of a midpoint 4. JK = JL ~ 4. Given 5. JM = JM ~ 5. Reflexive Property 6. JMK = JML ~ 6. SSS 7. < K = <L ~ 7. CPCTC

Use the Isosceles Triangle Theorem

Converse of the Isosceles Triangle Theorem (Converse of the Base Angles Theorem) If two angles of a triangle are congruent, then the sides opposite them are congruent B C A

Corollaries If a triangle is equilateral, then it is equiangular If a triangle is equiangular, then it is equilateral If a triangle is equilateral (and equiangular) then it is a regular triangle If a triangle is equilateral (and equiangular) then the angles are 60°

Homework Page 267/1, 2, 4-6, 8-10, 12-14, 19, 26-29, 35, 36, 52, 54, 56