Isosceles Triangles Sec: 4.6 Sol: G.5

Properties of Isosceles Triangles An isosceles triangle is a triangle with two congruent sides. The congruent sides are called legs and the third side is called the base. 3 Leg Base 2 1 Vertex Base Angles

Theorem 4.9 Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides (base angles) are congruent. A B C

Given: Prove: Statement Reason 1. 2. 3. 4. 5.

Find the measure of the missing angle If What is the measure of

Lesson 3-2: Isosceles Triangle Theorem 4.10 If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C Example: Find the value of x. Since two angles are congruent, the sides opposite these angles must be congruent. 3x – 7 = x + 15 2x = 22 X = 11 50 ° 3x - 7 x+15 A B C Lesson 3-2: Isosceles Triangle

Example: Name Two Congruent Angles: Name Two Congruent Segments:

Properties of Equilateral Triangles Corollaries: 4.3 A triangle is equilateral if and only if it is equiangular. 4.4 Each angle of an equilateral triangle measures 60°. 60° 60° 60°

Example: Triangle EFG is equilateral, and segment EH bisects angle E Find the measure of angle 1 and 2: Solve for X:

Assignments: Classwork: WB pg 51 1-6 Homework: Worksheet 4-6