Question

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

first figure pair: two rectangles (one vertical, one horizontal) on grid
congruent? ○ yes ○ no
similar? ○ yes ○ no

second figure pair: two circles (different sizes) on grid
congruent? ○ yes ○ no
similar? ○ yes ○ no

third figure pair: two l - shaped figures (different orientations) on grid
congruent? ○ yes ○ no
similar? ○ yes ○ no

fourth figure pair: two triangles (different orientations) on grid
congruent? ○ yes ○ no
similar? ○ yes ○ no

Explanation:

Step1: Analyze first figure pair

Congruent: Shapes have different side lengths (one is tall/skinny, one is short/wide), so not congruent.
Similar: Shapes are both rectangles, so their angles are equal, and side lengths are proportional.

Step2: Analyze second figure pair

Congruent: Circles have different radii, so not congruent.
Similar: All circles are similar (same shape, just scaled).

Step3: Analyze third figure pair

Congruent: Shapes have different overall dimensions (one is tall, one is wide), so not congruent.
Similar: Shapes have different angle/side proportionality (the "notch" creates different relative side ratios), so not similar.

Step4: Analyze fourth figure pair

Congruent: Triangles have different side lengths (one has vertical side 3, horizontal 2; the other has vertical 2, horizontal 3), so not congruent.
Similar: Triangles have different angle measures (side ratios are $\frac{3}{2}$ vs $\frac{2}{3}$, not equal), so angles don't match, not similar.

Answer:

1. First pair (rectangles):

Congruent? $\circ$ Yes $\bullet$ No
Similar? $\bullet$ Yes $\circ$ No

1. Second pair (circles):

Congruent? $\circ$ Yes $\bullet$ No
Similar? $\bullet$ Yes $\circ$ No

1. Third pair (notched shapes):

Congruent? $\circ$ Yes $\bullet$ No
Similar? $\circ$ Yes $\bullet$ No

1. Fourth pair (triangles):

Congruent? $\circ$ Yes $\bullet$ No
Similar? $\circ$ Yes $\bullet$ No