Download Isosceles and Equilateral Triangles

Isosceles and
Equilateral
Triangles
Section 5-1
Isosceles Triangle
• A triangle with at least two
congruent sides.
Vertex Angle
Leg
Leg
Base Angles
Base
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.