Triangle Angle-Bisector Theorem

Isosceles Triangle Theorems

Naming the Parts of

an Isosclees Triangle

Can you identify the base, the legs, the vertex, and the base angles?

Multiple Choice

Which segment is the base?

• Segment AB

• Segment BC

• Segment AC

Multiple Select

Which segments are the legs?

• Segment AB

• Segment BC

• Segment AC

Multiple Choice

Which angle is the vertex angle?

• $$\angle A$$

• $$\angle B$$

• $$\angle C$$

Multiple Select

Which angles are the base angle?

• $$\angle A$$

• $$\angle B$$

• $$\angle C$$

Isosceles Triangle Definition vs Theorem

Definition: Two or more congruent sides

Theorem: Base angles are congruent

  $\overline{EG}$  is FIVE different things!!

a) It is an altitude
b) it is an angle bisector
c) it is a perpendicular bisector
d) it is a median
d) it is a line of symmetry

There are many congruent pieces!!!

HOW MANY CONGRUENT
PAIRS CAN YOU FIND!!

Isosceles Triangle Theorems

• The base angles of an isosceles triangle are congruent

• The altitude to the vertex angle of an Isosceles triangle is also an angle bisector

• The altitude to the vertex angle of an Isosceles triangle is also a perpendicular bisector

Multiple Choice

Find the value of y.

• 5

• 10

• 15

• 20

Multiple Choice

Find the value of z.

• 5

• 10

• 15

• 20

Multiple Choice

Find the value of x.

• 43

• 86

• 94

• 47

Multiple Choice

Find the value of x.

• $$114\degree$$

• $$66\degree$$

• $$48\degree$$

• $$24\degree$$

Multiple Choice

Find the value of y.

• $$114\degree$$

• $$66\degree$$

• $$48\degree$$

• $$24\degree$$

Multiple Choice

Find the value of x

• 10

• 52

• 9

• 7

Multiple Choice

$$\angle1=20$$  What is the measure of  $$\angle A$$  

• 40

• 50

• 70

• 80

Multiple Choice

$$\angle B=40$$  What is the measure of  $$\angle1$$  

• 40

• 50

• 80

• 100

Multiple Choice

What is the measure of  $$\angle ADC$$  

• 40

• 50

• 80

• 90

Multiple Choice

AB = 100

How long is AD?

• 40

• 50

• 80

• 90

Multiple Choice

Triangle DEF is isosceles, angle D is the vertex angle,

DE = x + 7, DF = 3x – 1, and EF = 2x + 5.

Find the value of x.

(Hint: draw a picture)

• 2

• 4

• 6

• 8