Question

Trapezoid FGHI has vertices at (–4, 4), (–1, 4), (0, 2), and (–4, 2). Trapezoid F'G'H'I' has vertices at (0, –5), (0, 1), (4, 3), and (4, –5). Are these trapezoids similar? Why or why not?

A) no, the sides of the two trapezoids are not proportional to each other
B) yes, the sides of trapezoid FGHI are proportional to the sides of trapezoid F'G'H'I' by a scale factor of 2.
C) no, the angles and the shape of the two trapezoids are not the same
D) yes, the area of trapezoid FGHI is proportional to the area of trapezoid F'G'H'I' by a scale factor of 2.

Answer 1

A) Sides are not proportional

Explanation:

Let's rewrite the information given:

`"F(-4, 4)"` `->` `"F'(0,-5)`

`G(-1,4)` `->` `G'(0,1)`

`"H(0, 2)"` `->` `"H'(4,3)`

`"I(-4, 2)"` `->` `"I'(4,-5)`

Just from looking at these coordinates, I can tell that no common scale factor, or `k` was used. To check myself, I can set up a proportion for F and F'.

`color(blue)(-4/4=0/-5)`

`color(blue)(20!=0)`

When looking at these problems, eliminate any answer choices involving area. It has nothing to do with similarity, although you may be tempted to choose that answer (in this case, D). Always look for an answer choice involving side proportionality.

If there is no common scale factor between the points, sides are not in proportion.

A is correct.