Sec' 45 Isosceles

1
Sec. 4-5Isosceles Equilateral ?

• Objective
• 1) To use and apply properties of Isosceles
  Triangles.

2
Isosceles ? A ? with 2 ? sides

Vertex - ? formed by the two ? sides.
Isosceles means legs
Legs the two ? sides.
Base ?s The angles opposite of the legs.
Base the 3rd (non ?) side.
3
Isosceles ?
Did you get the last slide?

- ? formed by the two ? sides.
the two ? sides.
The angles opposite of the legs.
the 3rd (non ?) side.
4
Th(4 3) Isosceles ? Thm

• If 2 sides of a ? are ?, then the ?s opposite
  those sides are ?.

X
Y
Z
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Th(4 3) Isosceles ? Thm

• If 2 sides of a ? are ?, then the ?s opposite
  those sides are ?.
• Proof
• Given XB bisects ?YXZ
• XY ? XZ
• Prove ?Y ? ?Z

X
1
2
Y
Z
B
6
Statements 1) XY ? XZ 2) XB bisects ?YXZ 3) ?1
? ?2 4) XB ? XB 5) ?YXB ? ?ZXB 6) ?Y ? ?Z

• Reasons
• Given
• Given
• Def. of ? bisector
• Reflexive prop.
• SAS
• CPCTC

S
A
S
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Th(4-4) Converse of the Is. ? Thm.

• If 2 ?s of a ? are ?, then the sides opposite the
  ?s are ?.

B
If ?A ? ?C, then AB ? BC.
C
A
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Th(45)

• The bisector of the vertex of an isosceles ? is
  the ? bisector of the base.

If ?1 ? ?2, then
B
AD ? CD ?CDB and ?ADB are Right ?s ?CDB ? ?ADB
1
2
A
C
D
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Example

• If LM ? MN, then
• The ? is Isosceles
• If MO bisects ?LMN

M
1
Find the m?N, m?1 and m?2
m?N m?2 m?1
63 90 27
2
63
L
N
O
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Example 2

• m?BAC 80
• Find m?B

A
m
80
n
C
B
180 80 100 100/2 50 m?B
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Corollary A statement that follows
immediately from a theorem.

• C(4 - 3) If a ? is Equilateral, then the ? is
  Equiangular.
• C (4 4) If a ? is equiangular, then the ? is
  Equilateral.

60
12
Example 3 Solve for x
x