4.6 Isosceles, Equilateral and Right s

Isosceles triangle’s special parts

A is the vertex angle (opposite the base)

B and C are base angles (adjacent to the base)

A

BC

Leg

Leg

Base

Thm 4.6

Base s thm• If 2 sides of a are , then the s opposite them

are .( the base s of an isosceles are )

A

B C

If seg AB seg AC, then B C

) (

Thm 4.7

Converse of Base s thm• If 2 s of a are the sides opposite them are

.

) (

A

B C

If B C, then seg AB seg AC

Corollary to the base s thm

• If a triangle is equilateral, then it is equiangular. A

B C

If seg AB seg BC seg CA, then A B C

Corollary to converse of the base angles thm

• If a triangle is equiangular, then it is also equilateral.

)

)

(

A

BC

If A B C, then seg AB seg BC seg CA

Example: find x and y

• X=60

• Y=30

X Y120

Thm 4.8Hypotenuse-Leg (HL) thm

• If the hypotenuse and a leg of one right are to the hypotenuse and leg of another right , then the s are .

__

_ _

A

B C

X Y

Z

If seg AC seg XZ and seg BC seg YZ, then ABC XYZ

Given: D is the midpt of seg CE,

BCD and FED are rt s and seg BD seg FD.

Prove: BCD FED

B

CD

F

E

Proof

Statements

1. D is the midpt of seg

CE, BCD and

<FED are rt s and seg BD to seg FD

2. Seg CD seg ED

3. BCD FED

Reasons

1. Given

2. Def of a midpt

3. HL thm

Are the 2 triangles

)(

(

)

((

Yes, ASA or AAS

Find x and y.

75

x

x

y

2x + 75=180

2x=105

x=52.5 y=75

90

x

y60

x=60 y=30

Find x.

)

)

(

))

((

56ft

8xft

56=8x

7=x