Download Tutorial 12f - C on T ech Math : : An application

Isosceles Triangles
Tutorial 12f
Isosceles Triangles
• The congruent sides of an
isosceles triangle are the legs.
• The third side of an isosceles
triangle is the base.
• The two congruent sides form
the vertex angle.
• The other two angles are base
A
angles.
B
C
Legs = AB, BC
Vertex Angle = B
Base = AC
Base Angles = A, C
Isosceles Triangle
Theorem
• If two sides of a triangle are congruent,
then the angles opposite those sides are
also congruent.
C
A
If AC  BC, then A  B
B
Bisector Theorem
• The bisector of the vertex angle of an
isosceles triangle is the perpendicular
bisector of the base.
C
If AC  BC, and CD bisects ACB,
then CD  AB and CD bisects AB
A
D
B
Converse of Isosceles
Triangle Theorem
• If two angles of a triangle are congruent,
then the sides opposite the angles are
congruent.
C
A
If A  B, then AC  BC
B
Corollary to Isosceles
Triangle Theorem
• If a triangle is equilateral, then it is
equiangular.
If XY  YZ  ZX, then X  Y  Z
Y
X
Z
Corollary to Converse of
Isosceles Triangle Theorem
• If a triangle is equiangular, then it is
equilateral.
If X  Y  Z, then XY  YZ  ZX
Y
X
Z
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Check your answers
x = 39
y = 90
x = 62
y = 28
x = 67
y = 67
x = 31
y = 31
x = 79
y = 90
x = 64
y = 26