Download G Notes 4.5 Isosceles Triangles

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4.5 Isosceles and
Equilateral Triangles
Vertex angle
Isosceles Triangle
A triangle that has two
sides congruent
(called legs) and a
third side called a
base
base angles
Isosceles Triangle Theorem :
If 2 sides of a triangle are congruent, then the angles
opposite those sides are congruent.
D
E1
120
B
75
C
30
30
30
E
75
x
A
If DE  DC , BC  AC , and mCDE  120 ,
what is the measure of BAC ?
E2
E3
C
B
80 80
30
9
y
x
A
Find x.
x 9
mABC = 110
Find y.
y  20
Converse of Isosceles Triangle Theorem :
If 2 angles of a triangle are congruent, then the sides
opposite those angles are congruent.
M
A
P
R
N
Q
P
B
L
E3 Name 2 unmarked
congruent angles.
MLN  N
E4 Name 2 unmarked
congruent sides.
PL  PM
E5 Name 2 unmarked
congruent angles.
QAB  QBA
E6 Name 2 unmarked
congruent sides.
RA  RB
Equilateral
Triangle
A triangle that has
all three sides
congruent
A triangle is equilateral if and only if it is
Equilateral and equiangular
Each angle of an equilateral triangle measures
60
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PWS 4.5 Omit 20 & 24