Similar and congruent worksheet worksheets library - Free Printable

Since I can't view or access images directly, I can’t see the specific shapes in your uploaded image. However, based on the text you've provided, I can help you solve the "Congruent and Similar Shapes" worksheet (Lesson 32) by explaining how to determine whether pairs of shapes are congruent or similar, and then guide you through each problem.

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🔷 Definitions:

- Congruent shapes: Same shape and same size. They can be rotated or flipped, but they must match exactly.
- Similar shapes: Same shape, but different sizes. They are proportional (one is a scaled version of the other).

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Now, let’s go through each pair from the worksheet:

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1. Two rectangles

- If both rectangles have the same length and width, they are congruent.
- If they have the same proportions but different sizes, they are similar.
- But if one rectangle is clearly larger than the other, yet has the same shape (e.g., both are 2x4), they are similar.
- If they are identical in size and shape → congruent.

✔ Answer: Check if dimensions are equal.
👉 If same size → Congruent
👉 If same shape, different size → Similar

> ⚠️ Without seeing the image, assume:
> If both rectangles look identical → Congruent
> If one is bigger → Similar

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2. Two stars

- Stars are often used as examples of similar shapes.
- If both stars have the same number of points and same angles, but one is smaller → Similar.
- If they are exactly the same size and shape → Congruent.

✔ Answer: Likely Similar (commonly shown in such worksheets), unless they are identical.

> 👉 Answer: Similar (assuming same shape, different size)

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3. Two triangles

- One triangle is upright, the other is tilted.
- If their sides and angles match (just rotated), they are congruent.
- If one is larger than the other, even with same angles → Similar.

✔ Answer: If same size, just rotated → Congruent
If one is larger → Similar

> 👉 Most likely Congruent (since rotation doesn’t affect congruence)

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4. Trapezoid and another trapezoid

- Look at the shape: Are the bases and legs proportionally the same?
- If one is a scaled-up version of the other → Similar.
- If they are the same size and shape → Congruent.

✔ Answer: If one is larger, but same shape → Similar
If identical → Congruent

> 👉 Often in these problems, this pair is Similar (different sizes)

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5. Two circles

- All circles are similar because they have the same shape regardless of size.
- But only congruent if they have the same radius.

✔ Answer:
- If same size → Congruent
- If different sizes → Similar

> 👉 Since they're two separate circles, likely Similar (unless explicitly same size)

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6. Two squares

- Squares are always similar (all angles 90°, all sides equal).
- But only congruent if side lengths are equal.

✔ Answer:
- If same size → Congruent
- If different sizes → Similar

> 👉 Usually in such exercises, one square is smaller → Similar

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✔ Final Answers (Based on Common Worksheet Patterns):

| # | Answer |
|---|---------------|
| 1 | Congruent |
| 2 | Similar |
| 3 | Congruent |
| 4 | Similar |
| 5 | Similar |
| 6 | Similar |

> 💡 Note: For #1, if the rectangles are different sizes, it should be Similar. But since the shapes appear identical in many versions, Congruent is common.

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🧠 Tips for Solving:

- Congruent = Same shape + same size
- Similar = Same shape + possibly different size
- Rotation/flip does not change congruence
- Circles and squares are always similar, but only congruent if same size

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If you can describe the shapes (e.g., “first pair: two rectangles, one is twice as big”) or send a text description, I can give exact answers!