4-5 Isosceles and Equilateral Triangles L.E.Q. How do you use and apply properties of isosceles triangles to solve problems?

Parts of an Isosceles Triangle. Between the 2 legs. Surround the base.

Theorem 4-3: Isosceles Triangle Theorem. If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.

Theorem 4-4: Converse of Isosceles Triangle Theorem. If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent.

Theorem 4-5: Vertex Angle Bisector Theorem. The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Example: Using the Isosceles Triangle Theorems.

Example: Using Algebra. Find the values of x and y.

A corollary is a statement that follows immediately from a theorem.

Corollary to Theorem 4-3. If a triangle is equilateral, then the triangle is equiangular.

Corollary to Theorem 4-4. If a triangle is equiangular, then the triangle is equilateral.

Homework: Pg 213-214 #s 3 – 16, 21-26 all.