Scale Factors with Ratios in Polygons

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

• 3.75

• 9.75

• 10

• 12

Determine if triangle KLM and triangle NOP are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

• The triangles are not similar.

• The triangles are similar because SSS (three sides proportional).

• The triangles are similar because AA (two angles congruent).

• The triangles are similar because SAS (two sides proportional, included angle congruent).

• The triangles are similar because SAS (two sides and included angle congruent).

Determine if triangle HIJ and triangle KLM are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

• The triangles are not similar.

• The triangles are similar because SSS (three sides proportional).

• The triangles are similar because SSS (three sides congruent).

• The triangles are similar because SAS (two sides proportional, included angle congruent).

• The triangles are similar because SAS (two sides and included angle congruent).

Determine if triangle JKL and triangle MNO are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

• The triangles are not similar.

• The triangles are similar because SSS (three sides proportional).

• The triangles are similar because SSS (three sides congruent).

• The triangles are similar because SAS (two sides proportional, included angle congruent).

• The triangles are similar because SAS (two sides and included angle congruent).

State if the polygons are similar.

• 1. The polygons ARE similar. 

• 1. The polygons are NOT similar because corresponding angles are not congruent.

• 1. The polygons are NOT similar because corresponding sides are not proportional. 

State if the polygons are similar.

• 1. The polygons ARE similar. 

• 1. The polygons are NOT similar because corresponding angles are not congruent.

• 1. The polygons are NOT similar because corresponding sides are not proportional. 

What is the scale factor of ΔABC to ΔDEF?

• 1/2

• 7/3

• 2

• 10/3

• 72

• 18

• 108

• 144

• 36

Match each term to the correct definition.

• scale factor

• a comparison of two quantities by division

• proportion

• an equation that states that two ratios are equal

• extended ratio

• compares more than two quantities and cannot be expressed as a single fraction 

• ratio

• a ratio, in simplest form, of corresponding side lengths between two similar figures; it essentially states how many times larger or smaller one figure is than the other

• extended proportion

• three or more equivalent ratios

Solve for x.

• 4

• 9

• 3

• 7