Isosceles and EquilateralTriangles

Section 5-1

Isosceles Triangle

• A triangle with at least two congruent sides.

LegLeg

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.