Geometry: Semester 2 Review

Triangles ABC and DEF are similar. Which of the following equations could be used to find the value of x. There are two.

Answer explanation

Corresponding sides of similar triangles form ratios that are equal - do you see which side goes with which?

If triangle DEF is a dilaton of triangle ABC, what was the scale factor used for the dilation?

• 14

Answer explanation

Since triangle DEF is an elargement, the scale factor must be greater than 1, so the side from the larger triangle goes in the numerator of the ratio.

Drag the points to show the dilation of the line y = -1.5x + 6 about the origin with a scale factor of 3.

Drag the points to show the dilation of the line y = -1.5x + 6 about the origin with a scale factor of 1/2.

Triangle P'R'Q' is a dialtion of triangle PRQ with the center of the dilation at the origin. What is the scale factor used in the dilation?

Answer explanation

R'Q' = 6 and RQ = 2, so the scale factor = 6/2 = 3

Triangle A'B'C' is a dilation of triangle ABC. What was the scale factor used in this dilation?

Answer explanation

A'B' = 14 and AB = 7, so the scale factor = 14/7 = 2.

Triangle A'B'C' is a dilation of triangle ABC. If the length of segment A'C' = 5.4, what is the length of segment AC?

Answer explanation

A'B' = 14 and AB = 7, so the scale factor = 14/7 = 2. 5.4/2 = 2.7.

Plot the midpoint of the segment with endpoints (-6, 2) and (2,4).

Then, plot the endpoint of the segment with endpoint (-6, 2) and midpoint (2, 4).

This student is using shadows to find the height of the tree. What scale factor could they use to find the height of the tree?

• 22.7

• 21.7

• 2.5

• 2

Answer explanation

To find how many times bigger the tree's shadow is than the student's shadow, compare the lengths using ratios. Make sure that the sides match up! In this case. match up the lengths of the shadows. 125/5.5

This student is using shadows to find the height of the tree. What calculation could they use to find the height of the tree?

Answer explanation

Since the scale factor si 125/5.5 = 22.7, multiply this by the peron's height.