Similarity Review first

Similarity Review first

Similar Figures

Figures are similar if:

Their corresponding angles are congruent

Their corresponding sides are proportional

AA~

• Two pairs of corresponding angles are congruent.

• If you don't have matching angles, they should add to 180.

Multiple Choice

Explain why the triangles are similar and solve for x.

• SSS~, 5.3

• AA~, 13.3

• SAS~, 13.3

• AA~5.3

SSS~

All three pairs of corresponding sides must have the same common ratio.

Multiple Choice

State the postulate used to show the triangles are similar.

• AA~

• SAS~

• SSS~

• none

Reading similarity statements

• Stack the triangle names

• Angles get 1 letter

• Sides get 2 letters. Remember, they can be named backwards sometimes!!

• Match the angles or sides vertically.

Writing Similarity statements given angles

• Rank the angles of the first triangle smallest to largest.

• Rank the angles of the second triangle smallest to largest.

• Name in that order!

Writing similarity statements given sides

• Rank the sides of each triangle from smallest to largest

• Find the opposite angle of each side.

• Name in that order!

Multiple Select

Which of the following is a correct similarity statement for the following triangles? Check all that apply.

• $\Delta SRT\sim\Delta MLN$

• $\Delta TSR\sim\Delta NML$

• $\Delta TRS\sim\Delta LNM$

• $\Delta RTS\sim\Delta NLM$

• $\Delta STR\sim\Delta MNL$

Multiple Choice

In the figure, are the triangles similar? If so, what is the common ratio?

• Not similar

• Similar. Common ratio is 2.

• Similar. Common ratio is 3.

• Similar. Common ratio is 6.

SAS~

• Two pairs of proportional sides

• An INCLUDED congruent angle.

• The angle must have both sides adjacent to it.

Multiple Select

In the figure shown, which TWO statements could prove that  $\Delta ATL\sim\Delta BWI\$  by SAS~?

•  $\angle A\cong\angle B$  

•  $\angle L\cong\angle I$  

•  $\angle T\cong\angle L$  

•  $\frac{AT}{BW}=\frac{WI}{TL}$  

•  $\frac{AL}{BI}=\frac{TL}{WI}$  

Multiple Choice

Are the two triangles similar? If so, what is the identity that proves it?

• Yes. SAS~

• Yes. AA~

• Yes. SSS~

• They are not similar.

Fill in the Blank

In the following figure,  $\Delta ORD\sim\Delta OKC$  .  Determine the value of x. 

Fill in the Blank

Given that

 $\Delta PHF\ \sim\ \Delta RIC,\$  
 $m\angle P\ =\ 114\degree$  
 $m\angle C\ =\ 23\degree$  
Determine  $m\angle H$  

Multiple Choice

Are these triangles similar?

State the reason

• Yes, by AA~

• Not similar

• Yes by SAS~

• Yes by SSS~

Multiple Choice

A flag stick on a golf course that is 6 1/2 feet tall casts a 9 3/4 foot shadow while a golfer nearby casts a 8 3/4 foot shadow. How tall is the golfer?

• 5 foot, 8 inches

• 5 foot, 9 inches

• 5 foot, 10 inches

• 5 foot, 11 inches

Multiple Choice

The Gateway Arch in Missouri casts a 120 foot shadow while a 16 foot pole casts a 4 foot shadow. How tall is the Arch?

• 30 feet

• 360 feet

• 480 feet

• 600 feet

Multiple Choice

Find the missing side in the similar figure above.

• 26

• 27.6

• 25.2

• 28.8

Multiple Choice

Which dimensions would produce a picture frame similar to the one shown above?

• 9 in by 12 in

• 4 in by 5 in

• 6 in by 8 in

• 12 in by 18 in

Multiple Choice

Based on the drawing, which of the following statements is true?

• The triangles are similar because the lengths of the sides are congruent.

• The triangles are not similar because the corresponding angles are not congruent.

• The triangles are similar because the corresponding angles are congruent.

• Can not determine if the triangles are similar because the scale factor is unknown.

Multiple Choice

State the postulate used to show the triangles are similar.

• AA~

• SAS~

• SSS~

• none