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Applied Geometry
Lesson: 6 – 4
Isosceles Triangles
Learn to identify and use properties of isosceles triangles.
Parts of an Isosceles
Isosceles Triangle
If two sides of a triangle are congruent,
then the angles opposite the sides are
Theorem 6-3
The median from the vertex angle of an
isosceles triangle lies on the
perpendicular bisector of the base and the
angle bisector of the vertex angle.
x = 49
y = 90
Because EG is also
a perpendicular bisector.
x = 65
y = 50
x = 90
y = 70
Converse of Isosceles
Triangle Theorem
If two angles of a triangle are congruent,
then the sides opposite those angles
are congruent.
mB  48
mA  mB  mC  180
48  48  mC  180
mC  84
4x = 6x - 5 AC = 4(2.5) = 10
-2x = -5
x = 2.5
BC = 6(2.5) -5 = 10
mC  84
AC  10
BC  10
Theorem 6-5
A triangle is equilateral if and only if it is
Pg. 249 1 – 5 all, 6 – 22 E