G8 - Lesson 6-10

G8 - Lesson 6-10

Angle-Angle Triangle Similarity

Objectives

• Angle-Angle Criterion

• Apply to solve problems involving similar triangles

 $\Delta ABC\ and\ \Delta QRS$  

•  $\angle ABC=\angle QRS$  

•  $\angle BCA=\angle QSR$  

• Triangle ABC and triangle QRS are similar

Angle-Angle (AA) Criterion

• If two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar triangles

•  $\angle A\cong\angle D$  

•  $\angle B\cong\angle E$  

•  $so\ \Delta ABC\sim\Delta DEF$  

Multiple Choice

Are the two triangles similar?

• Yes

• No

Multiple Choice

Is

 $\Delta QRS\sim\Delta QLM$  ?

• Yes

• No

Poll

Two equilateral triangles are always similar.

True or False?

• True

• False

Poll

Two right triangles are always similar.

True or False?

• True

• False

Poll

Two isosceles right triangles are always similar.

True or False?

• True

• False

Apply to solve problems involving similar triangles

 $\Delta ABC\sim\Delta EDC$  , what are the values of x and y?

Find x

• 2x + x = 180

• x = 60

Find y

•  $m\angle A=84\degree$  

•  $m\angle ACB\ =\ 60\degree$  

•  $m\angle A+m\angle B+m\angle ACB=180\degree$  

•  $84+3y+60=180$  

•  $y=12$  

Multiple Choice

Find the value of x if the two triangles are similar.

• 45

• 3

• 90

• 6

Multiple Choice

What is the value of x?

• 21

• 84

• 48

• 56