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Section 4.5 Isosceles & Equilateral Triangles
Geometry Class Notes
VOCABULARY:
Legs of Isosceles  : ___________________________________________________
Base of a Isosceles  : ____________________________________________________
Vertex  of an Isosceles  : _____________________________________________
Base  ' s of an Isosceles  : _______________________________________________
Parts of the Isosceles Triangle:
An isosceles  has symmetry about
a line through its vertex angle.
Theorem 4–3 Isosceles Triangle Theorem
Theorem 4–4 Converse of Isosceles Triangle Theorem
A  C
AB  BC
AB  BC
A  C
If ______ of a triangle are _____, then the
angles opposite those sides are _____.
If ______ of a triangle are _____, then the sides
opposite those angles are ______.
EXAMPLES:
A
_______________ a) Name the legs of the isosceles triangle.
B
1
2
_______________ b) Name the hypotenuse of the right triangle.
_______________ c) Name the base angles of the isosceles triangle.
3
4
5
D
C
EXAMPLES:
1.
Find the measures for the indicated variables below
2.
3.
x
n
100
50 y

54 
x
m
2
Corollary to Theorem 4-3
If
ABC
is equilateral:
____  ____  ____
Corollary to Theorem 4–4
If
ABC
is equiangular:
mA  ______  ,
mB  ______  ,
mC  ______ 
Then:
ABC is ___________
Then:
ABC is____________
EXAMPLES: Find x and the measure of each side of the triangles.
4. BLK is an isosceles triangle with a vertex
5.
FGH is equilateral with FG = x + 5, GH = 3x angle being K . If BL  2x  5 , LK  3x  13 ,
9, and FH = 2x - 2.
and BK  7x  15 , find the length of the base.
ABC is an isosceles with AB = BC
6.
LMN is isosceles,  L is the vertex angle, 7.
LM = 3x - 2, LN = 2x + 1, and MN = 5x - 2.
4x, BC = 3x + 2, and AC = 3x.
if AB =
Classify the following triangles.
8. Find the measure of each side of
ABC
with vertices A (-1, 5), B (6, 1), and C (2, -6).
9. In NGL with a perimeter of 68, NG = 3x + 8,
GL = 6x – 10, and LN = 2x – 7.