Similar Figures: Always, Sometimes, Never

Is this statement always, never, or sometimes true:

If two figures are congruent, then they are similar.

• Always

• Never

• Sometimes

Answer explanation

Cogruent figures are similar because the scale factor is 1.

Is this statement always, never, or sometimes true:

If two figures are similar, then they are congruent.

• Always

• Never

• Sometimes

Answer explanation

This is only true when the scale factor is 1 since multiplying the side lengths by 1 will not change them.

Is this statement always, never, or sometimes true:

If two figures have congruent corresponding angles, then the figures are similar.

• Always

• Never

• Sometimes

Answer explanation

This is only true for triangles. Angles are not enough for any other figure with four or more sides.

Is this statement always, never, or sometimes true:

If two triangles have at least 2 pairs of congruent, corresponding angles then they are similar.

• Always

• Never

• Sometimes

Answer explanation

Because all angles need to add up to 180 degrees, there is only one combination of angle measures if two are already known. Triangles are the only figures where angles are enough to determine similarity.

Is this statement always, never, or sometimes true:

If two figures have congruent corresponding angles and a common scale factor between corresponding sides, then the figures are similar.

• Always

• Never

• Sometimes

Answer explanation

This is the definition of similar figures.

Is this statement always, never, or sometimes true:

If there are two figures and you CANNOT dilate one figure to obtain the other then they are similar.

• Always

• Never

• Sometimes

Answer explanation

Similar figures are always scaled copies which means one can be dilated to obtain the other figure.

Is this statement always, never, or sometimes true:

Dilations change what kind of shape a figure is categorized (example: a dilation can change a rectangle to a trapezoid)

• Always

• Never

• Sometimes

Answer explanation

Dilations do not change angle measures nor add/subtract side lengths meaning they maintain whatever shape it is.

Is this statement always, never, or sometimes true:

Dilations keep angle measures the same no matter the scale factor.

• Always

• Never

• Sometimes

Answer explanation

This is part of the definition of similar figures.

Is this statement always, never, or sometimes true:

Similar figures have proportional side lengths no matter the scale factor.

• Always

• Never

• Sometimes

Answer explanation

This is part of the definition of similar figures.

Is this statement always, never, or sometimes true:

Triangles with one known pair of congruent, corresponding angles is enough information to determine if they are similar.

• Always

• Never

• Sometimes

Answer explanation

Triangles must have two pairs of congruent, corresponding angles to determine similarity, however, the exception is that one pair and proportional side lengths would be enough information.