4-5 Isosceles & Equilateral Triangles

1. Geometry Ms. Stawicki 4-5Isosceles & Equilateral Triangles

2. Objectives • 1) To use and apply properties of isosceles triangles

3. The Isosceles Triangle Theorems • The congruent sides of an isosceles triangle are its legs. • The third side is the base. • The two congruent sides form the vertex angle. • The other two angles are the baseangles. Vertex angle Leg Leg Base Base Angle Base Angle

4. Theorem 4-3: Isosceles Triangle Theorem • If two sides of a triangle are congruent, then the angles opposite those sides are congruent. • Theorem 4-4: Converse of Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite the angles are congruent. A B C A B C

5. Theorem 4-5: • The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C A B D

6. Corollary: a statement that follows immediately from a theorem. • In other words, taking a theorem one step further to apply to something else that follows the same concept of the theorem…. • In this case, we are taking the Isosceles Triangle Theorems & applying them to EQUILATERAL TRIANGLES

7. Corollaries to the Isosceles Triangle Theorem & its converse: • 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