Download Today you will Use properties of isosceles triangles and equilateral

Today you will
Use properties of isosceles triangles and equilateral triangles
to find missing dimensions of triangles.
Use CPCTC to prove corresponding parts of triangles
are =
4.6
Isosceles Triangles and Equilateral Triangles
base angle
leg
base
base angle
vertex angle
vertex
leg
Isosceles Triangle Theorem:
If 2 sides of a triangle are
those sides are .
, then the angles opposite
Converse of the Isosceles Triangle Theorem:
If two angles of a triangle are
those angles are
.
, then the sides opposite
2. Find m G
1. Find m F.
E
G
22o
D
x+44o
F
J
3xo
H
Corollaries for Equilateral Triangles
A triangle is equilateral IFF it is equiangular.
)
then
|
|
2.
)
Example: If
)
1.
|
o
Each angle of an equilateral triangle measures 60
2x+32o
(
Find x.
Find y.
5y-6
4y+12
B
Given:
Prove:
ABC is isosceles
EB bisects ABC
ABE
A
CBE
Statement
1.
ABC is isosceles
EB bisects ABC
E
Reason
1.
CPCTC:
Corresponding Parts of Congruent Triangles are Congruent
B
Given:
Prove:
ABC is isosceles
EB bisects ABC
AE
Statement
CE
A
E
C
Reason
Q
S
R
P
Given:
P
PX
RX
X
T
T
Y
Prove:
TY
RY
Statement
1.
PX
Reason
1.
T
P
TY
2.
PX = TY
2.
3.
XY = YX
3.
4.
PX + XY = PY and
TY + YX =TX
4.
5.
PY = TX
5.
6.
PY
6.
7.
RX
TX
7.
RY
8.
8.
9.
10.
Q
PQY
TSX
9.
10.
S
Given:
MS TR
MS = TR
Prove:
MA
M
R
A
TA
S
Statement
T
Reason