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4.6 The Isosceles
Triangle Theorems
Base Angles and Opposite Sides
Hypotenuse - Leg
Parts of an Isosceles Triangle
Vertex
leg
leg
base angle
base angle
base
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then
the angles opposite those sides are
congruent.
A
B
C
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the
angles opposite those sides are congruent.
Given: AB  AC
Bisect angle A BAD  CAD
A
So by SAS BAD  CAD
So
B  C
By C.P.C.T.
B
D
C
Corollary of Isosceles Triangle
Theorem
An equilateral triangle is also equiangular
An equilateral triangle has three 60 degree angles.
The bisector of the vertex angle of an
isosceles triangle is perpendicular to the
base at its midpoint.
Another Theorem
If two angles of a triangle are congruent,
then the sides opposite those angles are
congruent.
What is this compared to
the Isosceles Triangle Theorem?
An equiangular triangle is also equilateral.
Solve for x and y
50
y
x
Solve for angles… 2,3,4
Given: BC  AC
C 140
2
3
B
4
A
Hypotenuse – Leg (HL)
In two right triangles if the hypotenuse and
one leg are congruent, then the triangles
are congruent.
To use this you must show Right Triangles
Solve for v
2v  4
2v  2
v5
Find the missing side
62
42
56
41
62
Homework
Page 239 – 242
# 9 – 25 odd,
34 -37, 39
Homework
Page 239 – 242
# 8 -24 even
29- 33