Question

are the figures below congruent? (four sets of figures with congruent? label and yes/no radio buttons: first set - small right triangle and larger equilateral triangle; second set - two trapezoids; third set - two rectangles; fourth set - large circle and small circle)

Explanation:

Step1: Analyze Top - Right Pair

The top - right pair of figures: The two trapezoid - like (or triangle - like with a flat top) figures have the same shape and size. By the definition of congruent figures (figures that have the same shape and size, can be superimposed), these two figures are congruent. So we select "Yes" for the top - right.

Step2: Analyze Top - Left Pair

The top - left pair: One is a right - angled triangle and the other is an equilateral (or isosceles) triangle. Their shapes are different (one has a right angle, the other does not), so they are not congruent. We select "No" for the top - left.

Step3: Analyze Bottom - Right Pair

The bottom - right pair: One is a large circle and the other is a small circle. Their sizes are different, so they are not congruent. We select "No" for the bottom - right.

Step4: Analyze Bottom - Left Pair

The bottom - left pair: The two rectangles have the same shape and size. By the definition of congruent figures, they are congruent. We select "Yes" for the bottom - left.

Answer:

Top - Right: Yes; Top - Left: No; Bottom - Right: No; Bottom - Left: Yes