Identifying Similar and Congruent Shapes Worksheet | Free ... - Free Printable
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Step-by-step solution for: Identifying Similar and Congruent Shapes Worksheet | Free ...
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Step-by-step solution for: Identifying Similar and Congruent Shapes Worksheet | Free ...
Let's solve this step-by-step. The task is to determine whether each pair of shapes is similar, congruent, or neither.
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- Congruent: Shapes that are the same size and shape (can be rotated, reflected, or translated but not resized).
- Similar: Shapes that have the same shape but may differ in size (one is a scaled version of the other).
- Neither: If they are not the same shape and not proportional in size/shape.
We’ll go through each pair:
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- Same shape, same size.
- ✔ Congruent
> Answer: Congruent
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- Both are right-angled "L" shapes.
- One appears smaller than the other.
- They have the same angles and proportions → one is a scaled-down version.
- ✔ Similar
> Answer: Similar
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- Same shape, same size, different orientation (one flipped).
- Can be transformed via reflection.
- ✔ Congruent
> Answer: Congruent
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- Regular hexagons? Yes — both have six equal sides and angles.
- But one is clearly larger than the other.
- So same shape, different sizes → ✔ Similar
> Answer: Similar
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- Same shape, same size, just rotated.
- One points left, one right — rotation.
- ✔ Congruent
> Answer: Congruent
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- Same shape, same size, opposite direction.
- One is a rotation of the other.
- ✔ Congruent
> Answer: Congruent
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- One is larger, one is smaller.
- But both are trapezoids with same angles and proportions?
- Let’s see: the top and bottom bases seem proportional.
- Appears to be scaled down version.
- ✔ Similar
> Answer: Similar
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- One is larger than the other.
- Squares are always similar (all angles 90°, sides proportional).
- But not same size → ✔ Similar
> Answer: Similar
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- Same shape, same size.
- One is rotated (upside down), but still same dimensions.
- ✔ Congruent
> Answer: Congruent
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- One is solid, one is outlined.
- But shape is identical — just different color/stroke.
- Same size, same shape → ✔ Congruent
> Answer: Congruent
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- One is green equilateral triangle.
- Other is green rhombus-like shape? Wait — no.
- Actually, second shape has four sides — it’s a quadrilateral, not a triangle.
- So different number of sides → Not same shape.
- ✘ Neither
> Answer: Neither
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- One small yellow triangle.
- One large yellow triangle.
- Are they the same shape? Seems like both are right triangles.
- But angles appear different — one looks like a right triangle, the other might be isosceles.
- Wait — actually, look closely:
- First is small, acute? No — it looks like a right triangle.
- Second is a right triangle too, but longer leg.
- But if they are not proportional, then not similar.
- However, since one is clearly scaled-up version of the other, and angles match → ✔ Similar
Wait — actually, let's check: the second triangle has same angles as first — yes, both right triangles, and legs proportional?
From visual: seems like the second is a scaled version of the first.
So ✔ Similar
> Answer: Similar
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- Both are rectangles, same size, same shape.
- One is rotated? No — both upright.
- Same dimensions → ✔ Congruent
> Answer: Congruent
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- Both are slanted rectangles (parallelograms).
- Same shape, same size, one rotated slightly?
- Wait — both look identical in shape and size.
- Just one is shifted — so ✔ Congruent
> Answer: Congruent
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- First is a solid star.
- Second is a star with lines crossing, not filled.
- But shape: both are 5-pointed stars.
- But the second one is not the same shape — it's more like a star polygon with intersecting lines.
- The structure is different: one is a regular star, the other is an asterisk-like shape.
- So not same shape → ✘ Neither
> Answer: Neither
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- One is a crescent moon (curved).
- The other is a smaller arc, not closed.
- Different shapes: one is a lens-like shape, the other is a simple curve.
- Also, the second one doesn't close — it's not a full crescent.
- So not congruent, not similar → ✘ Neither
> Answer: Neither
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| # | Answer |
|---|------------|
| 1 | Congruent |
| 2 | Similar |
| 3 | Congruent |
| 4 | Similar |
| 5 | Congruent |
| 6 | Congruent |
| 7 | Similar |
| 8 | Similar |
| 9 | Congruent |
|10 | Congruent |
|11 | Neither |
|12 | Similar |
|13 | Congruent |
|14 | Congruent |
|15 | Neither |
|16 | Neither |
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✔ Final Answer Key:
1. Congruent
2. Similar
3. Congruent
4. Similar
5. Congruent
6. Congruent
7. Similar
8. Similar
9. Congruent
10. Congruent
11. Neither
12. Similar
13. Congruent
14. Congruent
15. Neither
16. Neither
---
Let me know if you'd like this formatted for printing or need explanations for any specific pair!
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Definitions:
- Congruent: Shapes that are the same size and shape (can be rotated, reflected, or translated but not resized).
- Similar: Shapes that have the same shape but may differ in size (one is a scaled version of the other).
- Neither: If they are not the same shape and not proportional in size/shape.
We’ll go through each pair:
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1) Two plus signs (+)
- Same shape, same size.
- ✔ Congruent
> Answer: Congruent
---
2) Two L-shaped polygons
- Both are right-angled "L" shapes.
- One appears smaller than the other.
- They have the same angles and proportions → one is a scaled-down version.
- ✔ Similar
> Answer: Similar
---
3) Two arrow-like shapes (chevrons)
- Same shape, same size, different orientation (one flipped).
- Can be transformed via reflection.
- ✔ Congruent
> Answer: Congruent
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4) Two hexagons
- Regular hexagons? Yes — both have six equal sides and angles.
- But one is clearly larger than the other.
- So same shape, different sizes → ✔ Similar
> Answer: Similar
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5) Two curved arrows (C-shapes)
- Same shape, same size, just rotated.
- One points left, one right — rotation.
- ✔ Congruent
> Answer: Congruent
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6) Two arrows: down and up
- Same shape, same size, opposite direction.
- One is a rotation of the other.
- ✔ Congruent
> Answer: Congruent
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7) Two trapezoids
- One is larger, one is smaller.
- But both are trapezoids with same angles and proportions?
- Let’s see: the top and bottom bases seem proportional.
- Appears to be scaled down version.
- ✔ Similar
> Answer: Similar
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8) Two squares
- One is larger than the other.
- Squares are always similar (all angles 90°, sides proportional).
- But not same size → ✔ Similar
> Answer: Similar
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9) Two semicircles
- Same shape, same size.
- One is rotated (upside down), but still same dimensions.
- ✔ Congruent
> Answer: Congruent
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10) Two curved arrows (U-shaped)
- One is solid, one is outlined.
- But shape is identical — just different color/stroke.
- Same size, same shape → ✔ Congruent
> Answer: Congruent
---
11) Two triangles
- One is green equilateral triangle.
- Other is green rhombus-like shape? Wait — no.
- Actually, second shape has four sides — it’s a quadrilateral, not a triangle.
- So different number of sides → Not same shape.
- ✘ Neither
> Answer: Neither
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12) Two triangles
- One small yellow triangle.
- One large yellow triangle.
- Are they the same shape? Seems like both are right triangles.
- But angles appear different — one looks like a right triangle, the other might be isosceles.
- Wait — actually, look closely:
- First is small, acute? No — it looks like a right triangle.
- Second is a right triangle too, but longer leg.
- But if they are not proportional, then not similar.
- However, since one is clearly scaled-up version of the other, and angles match → ✔ Similar
Wait — actually, let's check: the second triangle has same angles as first — yes, both right triangles, and legs proportional?
From visual: seems like the second is a scaled version of the first.
So ✔ Similar
> Answer: Similar
---
13) Two rectangles
- Both are rectangles, same size, same shape.
- One is rotated? No — both upright.
- Same dimensions → ✔ Congruent
> Answer: Congruent
---
14) Two parallelograms
- Both are slanted rectangles (parallelograms).
- Same shape, same size, one rotated slightly?
- Wait — both look identical in shape and size.
- Just one is shifted — so ✔ Congruent
> Answer: Congruent
---
15) Two stars
- First is a solid star.
- Second is a star with lines crossing, not filled.
- But shape: both are 5-pointed stars.
- But the second one is not the same shape — it's more like a star polygon with intersecting lines.
- The structure is different: one is a regular star, the other is an asterisk-like shape.
- So not same shape → ✘ Neither
> Answer: Neither
---
16) Two crescent shapes
- One is a crescent moon (curved).
- The other is a smaller arc, not closed.
- Different shapes: one is a lens-like shape, the other is a simple curve.
- Also, the second one doesn't close — it's not a full crescent.
- So not congruent, not similar → ✘ Neither
> Answer: Neither
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Final Answers:
| # | Answer |
|---|------------|
| 1 | Congruent |
| 2 | Similar |
| 3 | Congruent |
| 4 | Similar |
| 5 | Congruent |
| 6 | Congruent |
| 7 | Similar |
| 8 | Similar |
| 9 | Congruent |
|10 | Congruent |
|11 | Neither |
|12 | Similar |
|13 | Congruent |
|14 | Congruent |
|15 | Neither |
|16 | Neither |
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✔ Final Answer Key:
1. Congruent
2. Similar
3. Congruent
4. Similar
5. Congruent
6. Congruent
7. Similar
8. Similar
9. Congruent
10. Congruent
11. Neither
12. Similar
13. Congruent
14. Congruent
15. Neither
16. Neither
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Let me know if you'd like this formatted for printing or need explanations for any specific pair!
Parent Tip: Review the logic above to help your child master the concept of congruence and similarity worksheet.
