Bell Ringer

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Isosceles Triangles

Definitions

The two angles in an isosceles triangle adjacent to the base of the triangle are called base angles.

The angle opposite the base is called the vertex angle.

Base Angle Base Angle

Vertex Angle

Definitions - Review

ABC is an isosceles triangle.

A C

B Name each item(s):

Vertex Angle

Base

Legs

Base Angles

B

AC

AB, CB

,A C

Side opposite C AB

Angle opposite BC A

?BAIs

A

C

B

AB

C

A

C

B

YesYes

No

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

A

C

B

Example 1

L N

M

Find the measure of each angle.

30om M

m L m N

x + x + 30o = 180o

2x + 30o = 180o

2x = 150o

x = 75o

75om L m N

Example 2Find the length of each side.

E

G

F

3x – 6

2x

6

3x – 6 = 6

3x = 12x = 4

EF = 6EG = 8

Example 3

O Q

P

Find the measure of each angle.

2 42

m P xm Q x

(2x – 4) + (x + 2) + (x + 2) = 180o

4x = 180o

x = 45o

2(45) 4 86

45 2 47

47

om Pom Qom O m Q

Hypotenuse-Leg (HL) Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

DEFABCthenDFACandEFBCIf ,

A

B C

D

E F

Practice

C

A B

M

N FP

- What do we still need to know to prove the triangles are congruent?

Practice Find the measure of the missing angles and

tell which theorems you used.

50°A

B

CA

B

C

You try!Is there enough information to prove the

triangles are congruent?

S

R

T

UV

W

YesNo No

2x

2xx

62