Question

which pairs of figures are congruent? which pairs are similar?

Explanation:

Step1: Recall the definitions

Congruent figures have the same shape and size. Similar figures have the same shape but not necessarily the same size.

Step2: Analyze the first pair (L - shaped figures)

The two L - shaped figures are not the same size (one is larger than the other), so they are not congruent. But they have the same shape, so they are similar.

Step3: Analyze the second pair (circles)

The two circles are not the same size (one is larger than the other), so they are not congruent. But all circles are similar (since the ratio of their radii is a constant for similarity of circles and they have the same shape), so they are similar.

Step4: Analyze the third pair (rectangle and square)

A rectangle and a square have different shapes (a square has all sides equal, a rectangle has opposite sides equal). So they are neither congruent nor similar.

Step5: Analyze the fourth pair (triangles)

The two triangles have the same shape (they are both triangles and the angles are in proportion as per the similarity criteria for triangles, assuming they are equiangular which is implied by the similar - looking shape in a basic geometric sense for such problems). But they are not the same size. So they are not congruent but are similar.

Answer:

First pair: Congruent? No, Similar? Yes.
Second pair: Congruent? No, Similar? Yes.
Third pair: Congruent? No, Similar? No.
Fourth pair: Congruent? No, Similar? Yes.