Introduction to Corresponding Parts of Similar Triangles

Similar Triangles

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• Corresponding Angles are CONGRUENT

• Corresponding Sides are PROPORTIONAL

​Similar Shapes are the result of a dilation

Criteria for Similar Shapes

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Multiple Choice

Which of the below is the only correct similarity statement for the two triangles?

• $$\Delta SKE\sim\Delta THC$$  

• $$\Delta SKE\sim\Delta TCH$$  

• $$\Delta SKE\sim\Delta CHT$$  

• $$\Delta SKE\sim\Delta HCT$$  

Multiple Choice

These two quadrilaterals are similar. Based on the image, what is the correct similarity statement?

• $$JKLM\ \sim\ NOPQ$$

• $$KLMJ\ \sim\ NOPQ$$

• $$LMJK\ \sim\ PQNO$$

• $$LKMJ\ \sim\ ONQP$$

Multiple Choice

Use the similarity statement to answer the following:

<F = ___

• <H

• <I

• <G

• not congruent to another angle

Multiple Choice

Complete the similarity statement.

• OEG

• OGE

• EGO

• GOE

Multiple Choice

What is the similarity statement for the triangle pair?

• ΔXYZ is similar to ΔNEW

• ΔXZY is similar to ΔNWE

• ΔZYX is similar to ΔENW

• ΔYZX is similar to ΔNWE

Multiple Choice

Complete the similarity statement.

$$\Delta ABC\ is\ similar\ to\ .....$$  

• $$\Delta PQS$$  

• $$\Delta SPQ$$  

• $$\Delta QPS$$  

• they are not similar

Multiple Choice

$$\Delta PQR\ is\ similar\ to\ \Delta STU$$  What side corresponds to side UT?

• PQ

• RQ

• QR

• QP

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Hypotenuse

• The longest side of a right triangle

• The side that is opposite (across) from the 90^o angle.

• When using the Pythagorean Theorem, the Hypotenuse is represented by the variable, c.

Multiple Choice

What side(s) will always be the longest on a right triangle?

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Select

What side(s) will always be the shortest on a right triangle?

Select all that apply

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Multiple Choice

A rectangular pool at Andy's gym measures 25 m by 50 m. How far would Andy swim if he swims across the pool diagonally?

• 5 m

• 8.7 m

• 43.3 m

• 55.9 m

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°

• 90°

• 180°

• 360°

Multiple Choice

Find the measure of the missing angle.

• 90^o

• 10⁰

• 130^o

• 50^o

Multiple Choice

Which equation can be created to solve for the value of x in the triangle?

• $$x+53=x+68$$  

• $$x+53+75=180$$  

• $$x+53+x+68+75=180$$  

• $$x+53+x+68=75$$  

Multiple Choice

Solve for x.

• 16

• 11

• 50

• 6

Multiple Choice

Solve for x THEN find the degrees for angle A.

• 44^o

• 96^o

• -14^o

• 63^o

Multiple Choice

Find the measure of the indicated angle. 

• 34

• 46

• 62

• 36

If two angles of one triangle are congruent to the corresponding angles of another triangle, the triangles are similar.

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​​Angle Angle Similarity Theorem (AA):

Multiple Select

Which of these triangle pairs can be proven similar using AA? Mark all that apply.

Multiple Choice

Are the triangles similar?

• Yes

• No

Multiple Choice

Are the triangles similar?

• Yes

• No

Multiple Choice

Which triangles are similar to triangle A?

• B

• C

• Both

• None

Multiple Choice

Which triangles are similar to triangle A?

• B

• C

• Both

• None

Multiple Choice

Find the measure of the indicated angle. 

• 145 degrees

• 24 degrees

• 20 degrees 

• 21 degrees

Multiple Choice

Which statement shows these triangles are similar by AA~?

• $$\Delta TRS\sim\Delta QPR$$  

• $$\Delta RST\sim\Delta RPQ$$  

• $$\angle STR\cong\angle PQR$$  

Multiple Choice

Are these triangles similar?

• No, they are not similar

• Not Enough Information 

• Yes, similar by AA~ 

Multiple Choice

Are these triangles similar?

• No, they are not similar

• Not Enough Information 

• Yes, similar by AA~ 

Multiple Choice

Are these triangles similar?

• No, they are not similar

• Not Enough Information 

• Yes, similar by AA~ 

Multiple Choice

Are these triangles similar?

• No, they are not similar

• Not Enough Information 

• Yes, similar by AA~ 

Multiple Choice

Are these triangles similar?

• No, they are not similar

• Not Enough Information 

• Yes, similar by AA~