Question

Jason says that all rectangles are similar because any two rectangles he chooses have 4 pairs of congruent corresponding angles. Gabby says Jason is wrong. Who is correct? Explain your answer.

Answer 1

Jason is right while Gabby is wrong because, two congruent rectangles are similar, but two similar rectangles may not be congruent.

For two figures to be considered similar, the following criterion must be satisfied:

• All corresponding angles must be congruent.

This means the only criterion necessary for two figures to be considered congruent is that they must have the same shape but not necessary the same size. i.e. equal corresponding angles and the same ratio of corresponding lengths.

On the other hand, for two figures to be considered congruent, the following must be satisficed:

• Have equal corresponding side lengths
• Have equal corresponding angles

This implies that they must have the same shape and size.

Thus, if two rectangles have the 4 pairs of corresponding angles that are congruent, they are said to be similar.

The diagram of two similar rectangles is shown in the image attached below.

Therefore, Jason is right: all rectangles are similar.

Learn more about rectangles here:

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