Ratio and Similar Figures

A gate casts a shadow that is 5 ft long.  A nearby cactus is 9 ft tall and casts a shadow that is 15 ft long.  What is the height of the gate?

• 27 ft

• 3 ft

• 12 ft

• 45 ft

Katie went to Kinko’s Copy Center to reduce her rectangular design that is 32 in wide and 40.5 in long.  If the new width is 6.4 in, what is the length of the reduced design?

• 8.1 in

• 4.2 in

• 5 in

• 9 in

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75

• 9.75

• 10

• 12

• A
• B
• C
• D

A picture of a school’s mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 54 in., what is the length of the banner? 

• 72 in

• 60 in

• 62 in

• 80 in

The pair of figures is similar. Find the missing side.

• x = 9

• x = 28

• x = 7

• x = 63

Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

All corresponding sides are proportional (same ratio) in similar figures.

• True

• False

Two objects that are the same shape but not the same size are _______.

• Congruent

• Vertical

• Similar

• Complementary 

All angles in similar figures are congruent.  

• True

• False