Question

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

Explanation:

Step1: Analyze top-left shapes

Check congruence (same size/shape): The rectangle and tall rectangle have different side lengths, so not congruent. Check similarity (same shape, scaled): Both are rectangles, angles equal, sides proportional ($\frac{2}{1}=\frac{4}{2}=2$).

Step2: Analyze top-right shapes

Check congruence: Triangles have different side lengths, not congruent. Check similarity: Angles are equal, sides proportional ($\frac{3}{1}=\frac{2}{1}\times1.5$? No, wait: vertical side 3 vs 1, horizontal side 2 vs 1, ratio $\frac{3}{1}=3$, $\frac{2}{1}=2$ → not equal. Wait no, correct: triangles have right angles, other angles match? No, side ratios are not equal, so not similar? Wait no, recheck: top triangle has legs 3 and 2, bottom has legs 1 and 1. Ratios $\frac{3}{1}
eq\frac{2}{1}$, so angles are different. So not congruent, not similar.

Step3: Analyze bottom-left shapes

Check congruence: Circles have different radii, not congruent. Check similarity: All circles are similar (same shape, scaled).

Step4: Analyze bottom-right shapes

Check congruence: Shapes have different sizes and modified structure, not congruent. Check similarity: Shapes do not have proportional corresponding sides or matching angles, so not similar.

Answer:

1. Top-left:

Congruent? ○ Yes ● No
Similar? ● Yes ○ No

1. Top-right:

Congruent? ○ Yes ● No
Similar? ○ Yes ● No

1. Bottom-left:

Congruent? ○ Yes ● No
Similar? ● Yes ○ No

1. Bottom-right:

Congruent? ○ Yes ● No
Similar? ○ Yes ● No