Identifying Similar and Congruent Shapes worksheet for math education.

Let's solve each of the 16 problems on this worksheet by determining whether the shapes are similar, congruent, or neither.

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🔷 Definitions:

- Congruent: Same shape and same size (can be rotated or flipped).
- Similar: Same shape but different sizes (one is a scaled version of the other).
- Neither: Different shapes or not proportional.

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Now, let’s go through each pair:

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1)

Two pink L-shaped figures.
✔ Same shape and size — just one is rotated.
→ Congruent

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2)

Two blue arrow-like shapes.
One is flipped and rotated, but same shape and size.
→ Congruent

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3)

Two purple pentagon-like shapes with a notch.
One is smaller than the other, but same shape.
→ Similar

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4)

Two green pentagons.
Same shape and size? No — one appears to be larger.
Wait: actually, both have same proportions and angles. But sizes differ — one is clearly bigger.
→ Similar

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5)

Two purple "star" or "cross" shapes with rounded edges.
Same shape, different sizes — one is much larger.
→ Similar

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6)

Two yellow trapezoids.
One is smaller, but same shape.
→ Similar

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7)

Two orange plus signs.
Same shape and size — just one is rotated.
→ Congruent

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8)

Two curved crescent shapes.
Same shape and size — just mirrored.
→ Congruent

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9)

Blue square vs. blue rectangle.
Different shapes — one is square, other is rectangle.
→ Neither

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10)

Red triangle vs. small red right triangle.
Are they similar? The big one looks like a right triangle, small one too. But are they scaled versions?
But wait: the small one is not a scaled version — it has different proportions.
Actually, both appear to be right triangles, but unless angles and sides are proportional, not similar.
Looking closely: the large one is equilateral-looking? Wait — no, it's a right triangle. Small one is also a right triangle. But if the angles are same, then similar.
But in this case, the small one seems to have same angles, just smaller.
Assuming they're both right triangles with same angles → Similar

But wait — the small triangle is not a scaled-down version of the large one? Let's check:
The large triangle is a right triangle, the small one is also a right triangle, but from visual inspection, the angles appear the same — so likely similar.

→ Similar

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11)

Two green L-shapes.
Same shape and size — just one is rotated.
→ Congruent

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12)

Two pink trapezoids.
Same shape and size? Yes — identical.
→ Congruent

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13)

Two light blue curved rectangles.
One is wider, one is narrower — but same shape?
No — they’re both curved rectangles, but proportions differ.
Not scaled versions — one is shorter and wider.
→ Neither

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14)

Two orange quadrilaterals.
Same shape and size? One is rotated, but look same.
Yes — same shape and size.
→ Congruent

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15)

Two purple circles.
Same shape, different sizes?
Yes — one is smaller.
But all circles are similar (same shape), but only congruent if same size.
These are different sizes → Similar

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16)

Two orange arrow-like shapes.
Same shape, but one is rotated and possibly flipped.
Size appears same.
→ Congruent

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✔ Final Answers:

| # | Answer |
|---|------------|
| 1 | Congruent |
| 2 | Congruent |
| 3 | Similar |
| 4 | Similar |
| 5 | Similar |
| 6 | Similar |
| 7 | Congruent |
| 8 | Congruent |
| 9 | Neither |
|10 | Similar |
|11 | Congruent |
|12 | Congruent |
|13 | Neither |
|14 | Congruent |
|15 | Similar |
|16 | Congruent |

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📝 Summary:

- Congruent: 1, 2, 7, 8, 11, 12, 14, 16 → 8 items
- Similar: 3, 4, 5, 6, 10, 15 → 6 items
- Neither: 9, 13 → 2 items

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✔ Answer Key:

```
1. Congruent
2. Congruent
3. Similar
4. Similar
5. Similar
6. Similar
7. Congruent
8. Congruent
9. Neither
10. Similar
11. Congruent
12. Congruent
13. Neither
14. Congruent
15. Similar
16. Congruent
```

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