Question

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

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:

First Figure (Two Circles)

Step1: Check Congruence

Congruent figures have same shape and size. The two circles look same size? Wait, no—wait, maybe they are same? Wait, no, maybe I missee. Wait, congruent: same shape and size. If the two circles have same radius, then congruent. Similar: same shape (all circles are similar). So for congruent: if they are same size, yes. But maybe in the grid, they are same? Wait, maybe the first pair: two circles. So congruent? Let's see: if they are same size, yes. Similar: yes, because all circles are similar.

Step2: Check Similarity

All circles are similar (same shape, different sizes or same size). So similar is yes.

Second Figure (Two L - Shapes)

Step1: Check Congruence

Congruent: same shape and size. The big L and small L—different sizes, so congruent? No. Similar: same shape (L - shape), so similar? Yes, because they have same shape (proportional sides, same angles).

Third Figure (Two Rectangles)

Step1: Check Congruence

Congruent: same shape and size. The first rectangle is tall and thin, the second is wide and short. Different sizes and proportions? Wait, no—wait, maybe their dimensions. Suppose first rectangle: height 4, width 1; second: height 2, width 3? No, maybe not. So congruent? No. Similar: similar rectangles have length/width ratio same. If first is height 3, width 1; second height 2, width 3—ratios 3/1 and 2/3, not same. So similar? No.

Fourth Figure (Two Triangles)

Step1: Check Congruence

Congruent: same shape and size. The two triangles—one looks like a right triangle, the other? Wait, maybe one is a right triangle, the other not? Wait, no—wait, maybe their angles. If one is a right triangle and the other not, or different angles. Wait, maybe the first triangle has base 3, height 1; second base 2, height 1—different shapes. So congruent? No. Similar: similar triangles have same angles. If their angles are different, not similar. So similar? No. Wait, maybe I made a mistake. Let's re - evaluate:

Answer:

First Pair (Circles):
Congruent: Yes (if same size) / No? Wait, maybe in the grid, they are same. Let's assume:
Congruent: Yes; Similar: Yes

Second Pair (L - Shapes):
Congruent: No; Similar: Yes

Third Pair (Rectangles):
Congruent: No; Similar: No

Fourth Pair (Triangles):
Congruent: No; Similar: No

Wait, but maybe the first pair: two circles—congruent (yes), similar (yes). Second: L - shapes—congruent (no), similar (yes). Third: rectangles—congruent (no), similar (no). Fourth: triangles—congruent (no), similar (no).

But let's present each:

1. Two Circles:

Congruent? Yes
Similar? Yes

1. Two L - Shapes:

Congruent? No
Similar? Yes

1. Two Rectangles:

Congruent? No
Similar? No

1. Two Triangles:

Congruent? No
Similar? No

Wait, but maybe the first pair of circles: if they are same size, congruent (yes), similar (yes). The L - shapes: same shape (proportional), so similar (yes), congruent (no). The rectangles: different proportions, so not similar (no), not congruent (no). The triangles: different shapes, so not similar (no), not congruent (no).

So final answers:

First pair:
Congruent: Yes
Similar: Yes

Second pair:
Congruent: No
Similar: Yes

Third pair:
Congruent: No
Similar: No

Fourth pair:
Congruent: No
Similar: No