Question

which pairs of figures are congruent? which pairs are similar?
(image of four groups of figures with congruent and similar options for each group)
first group (two squares):
congruent? ● yes ○ no
similar? ● yes ○ no
second group (two triangles):
congruent? ○ yes ● no
similar? ○ yes ● no
third group (two l - shaped figures):
congruent? ○ yes ● no
similar? ○ yes ● no
fourth group (a circle and an ellipse):
congruent? ○ yes ● no
similar? ○ yes ● no

Explanation:

First Pair (Two Squares)

Step1: Analyze Congruence

Congruent figures have same shape and size. The two squares have same side lengths (from grid), so congruent (Yes).

Step2: Analyze Similarity

Similar figures have same shape (proportional sides, equal angles). Squares have all angles \(90^\circ\), sides proportional (ratio \(1:1\)), so similar (Yes).

Second Pair (Two Triangles)

Step1: Analyze Congruence

The triangles have different sizes (from grid), so not congruent (No).

Step2: Analyze Similarity

For similarity, angles must be equal and sides proportional. The larger triangle and smaller triangle: check angles (both right? No, one is a taller triangle, the other smaller—angles not equal? Wait, no, maybe the user's initial selection: the smaller triangle and larger—if their angles are not equal (e.g., one is a different type), so not similar (No).

Third Pair (Two L - shaped Figures)

Step1: Analyze Congruence

The two L - shaped figures: one is rotated, but check size. From grid, do they have same area/side lengths? The first L and the rotated L—maybe different sizes? So not congruent (No).

Step2: Analyze Similarity

Similarity requires same shape (proportional sides, equal angles). The two L - shapes: do their corresponding sides have same ratio? If not, and angles not all equal, so not similar (No).

Fourth Pair (Circle and Ellipse)

Answer:

s:

• First Pair: Congruent? Yes; Similar? Yes
• Second Pair: Congruent? No; Similar? No
• Third Pair: Congruent? No; Similar? No
• Fourth Pair: Congruent? No; Similar? No