Download Section 4.6 Isosceles and Equilateral Triangle Notes

Geometry
S e c t io n 4 . 6
Name:
D ate :
I s o s c e le s a n d E q u ila t e r a l T r ia n g le N o t e s
In this lesson you will
use properties of isosceles triangles.
use properties of equilateral triangles.
Vertex Angle
A
Isosceles Triangle
Leg
Equilateral Triangle
Leg
Base Angle
Base Angle
B
C
Base
You learned that an isosceles triangle has exactly 2 equal sides called the _______, and a 3rd side called the ______.
•
The two angles adjacent to the base are the ________ angles.
•
The angle opposite the based is the ____________ angle.
Theorem
Description
Isosceles Triangle
Theorem
If two sides of one triangle are
congruent then
Diagram/Picture
.
Converse of
Isosceles Triangle
Theorem
If two angles of one triangle are
congruent then
Equilateral
Triangle Theorem
If a triangle is equilateral then
Equiangular
Triangle Theorem
If a triangle is equiangular then
.
Check your progress p. 284 # 1A, 1B
.
Important Characteristics
Example 1: Find the value of x and y.
Example 2: Find x, GE and EF.
G
x°
36
5x - 9
y°
62°
y=
x=
E
x=
Example 3: Find the value of x and y .
GE=
EF=
Example 4: Find x, AB and BC .
y°
B
6x + 7
50 °
F
3x + 9
4x -3
x°
A
C
3x + 16
x=
y=
x=
AB=
BC=
x=
y=
z=
Example 5: Find the value of x, y, and z.
x°
y°
50 °
z°
Check your progress p. 285 # 2A, 2B, 3
Example 6:
X
a) Name the side opposite ∠Y
b) Name the side opposite ∠X
c) Name the angle opposite side XY
d) Name the angle opposite side YZ
e) XY and YZ include what angle?
f) XZ and YZ include what angle?
Y
Z