Download 4.5 Isosceles and Equilateral Triangles

4.5 Isosceles and Equilateral
Triangles
Isosceles Triangles
•At least two sides are of equal length.
•It also has two congruent angles.
Vertex Angle
Legs
Base
Base Angles
Isosceles Triangle Theorem
 If two sides of a triangle are congruent, the angles
opposite them are congruent.
IF : AB  AC
THEN : B  C
Converse of Isosceles Triangle Theorem
 If two angles of a triangle are congruent, the sides
opposite them are congruent
IF : B  C
THEN : AB  AC
 The bisector of the vertex angle of an isosceles
triangle is the perpendicular bisector of the base
CD  AB
and
CD bisects AB
Corollary to Theorem 4.3
 If a triangle is equilateral, then the triangle is
equiangular
x
X  Y  Z
Y
Z
Corollary to Theorem 4.4
 If a triangle is equiangular, then the triangle is
equilateral
x
XY  YZ  ZX
Y
Z