Download 4-8 (label picture with parts below) ______: [of an isosceles triangle

4-8
(label picture with parts below)
__________: [of an isosceles triangle] one of the two congruent sides of the isosceles triangle
__________________________: [of an isosceles triangle] the angle formed by the legs of an
isosceles triangle
____________: [of an isosceles triangle] the side opposite the vertex angle
__________________________: [of an isosceles triangle] one of the two angles that have the
base of the triangle as a side
Theorem
Isosceles Triangle Theorem:
If two sides of a triangle are congruent, then
the angles opposite the sides are congruent.
Hypothesis
Conclusion
B
Converse of Isosceles Triangle Theorem:
If two angles of a triangle are congruent, then
the sides opposite those angles are congruent.
C
___
___
DE
DF
___
___
Ex. 1: The length of YX is 20 feet. Explain why the length of YZ is the same.
___
m YZX = 180° - ____° = ____°, so XY
___
YZ by ____________________
__________________________________
Thus YZ = _____ feet
Ex. 2: Find each angle measure.
A.) m F
180 – 22 = _____°  the sum of the two angle
measures at the base of the triangle
__
__
because DE
EF, the angles opposite them are congruent by the
_____________________________,  ______°/2 = ____° each  m F = _____°
B.) m G
__
because GH
__
HJ, the angles opposite them are congruent by the
____________________________  _______ = 3x
(solve for x)
m G = x + 44
=
=
Equilateral Triangle:
If a triangle is equilateral, then it is
equiangular. (equilateral  equiangular)
Equiangular Triangle:
If a triangle is equiangular, then it is
equilateral. (equiangular  equilateral)
A
B
C
___
___
___
DE
DF
EF
Ex. 3: Find each value.
A.) x
equilateral (all three sides congruent)  equiangular (all three angles congruent)
_________________ = 60°
x=
B.) y
equiangular (all three angles congruent)  equilateral (all three sides congruent)
5y – 6 =
y=