Isosceles and Equilateral Triangles Section 5-1

Isosceles Triangle A triangle with at least two congruent sides. Leg Leg Base Vertex Angle Base Angles

Equilateral Triangle A triangle with all equal sides.

Theorems Theorem 5-1 (Isosceles Triangle Theorem) –The base angles of an isosceles triangle are congruent Theorem 5-2 –The line of symmetry for an isosceles triangle 1. Bisects the vertex angle 2. Is the perpendicular bisector of the base.

Theorems (con’t) Theorem 5-3 –If two angles of a triangle are congruent, then the sides opposite those angles are congruent Theorem 5-4 –An equilateral triangle is also equiangular Theorem 5-6 –An equiangular triangle is also equilateral

Theorems (con’t) Theorem 5-5 –Each of the three lines of symmetry for an equilateral triangle bisects an angle of the triangle and is the perpendicular bisector of the side opposite that angle.