Question

congruent? yes no congruent? yes no similar? yes no similar? yes no congruent? yes no congruent? yes no similar? yes no similar? yes no

Explanation:

First pair (circle and ellipse)

• Congruent?

Congruent figures have the same shape and size. A circle and an ellipse have different shapes (a circle has all points at an equal distance from the center, while an ellipse has two foci and the sum of distances from any point on the ellipse to the two foci is constant). So, they are not congruent.

• Similar?

Similar figures have the same shape. Since a circle and an ellipse have different shapes (a circle is a special case of an ellipse with both foci at the same point, but in general, the ratios of their corresponding linear measures are not consistent in the way required for similarity), they are not similar.

Second pair (two T - shaped figures)

• Congruent?

Congruent figures have the same size. The two T - shaped figures are of different sizes. So, they are not congruent.

• Similar?

Similar figures have the same shape. The two T - shaped figures have the same shape (the ratio of the lengths of their corresponding sides is constant). So, they are similar.

Third pair (two rectangles)

• Congruent?

Congruent figures have the same size. Assuming the two rectangles have the same side lengths (if they are just placed side - by - side without any indication of size difference in the problem's visual), they are congruent.

• Similar?

Similar figures have the same shape. Since congruent figures are a special case of similar figures (with a scale factor of 1), they are similar.

Fourth pair (two triangles)

• Congruent?

Congruent figures have the same size. The two triangles are of different sizes. So, they are not congruent.

• Similar?

Similar figures have the same shape. The two triangles have the same shape (assuming they are both non - degenerate triangles and the angles are equal, which is a reasonable assumption for simple geometric figure similarity in basic problems). So, they are similar.

Answer:

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