Let's solve each question in
Section C of the "Congruent Shapes" worksheet. The task is to determine whether each pair of shapes are
congruent or not and provide a reason.
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🔷 What does "congruent" mean?
Two shapes are
congruent if they have the
same shape and size. This means:
- All corresponding sides are equal.
- All corresponding angles are equal.
- One shape can be transformed into the other using
translation, rotation, or reflection (no resizing).
> 🚫 If one shape is a
scaled version (larger or smaller) of the other, they are
not congruent, even if they are similar.
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✔ Question 1)
Shapes: Two yellow squares — one small, one large.
- The small square is clearly
smaller than the large one.
- Even though both are squares (same shape), their
sizes differ.
- Therefore, they are
not congruent.
🔹
Answer:
Not congruent because the shapes are different sizes (one is larger than the other). Congruent shapes must be identical in both shape and size.
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✔ Question 2)
Shapes: Two blue triangles — one upright, one rotated.
- Both appear to be
right-angled triangles.
- They look like they have the same side lengths and angles.
- The second triangle is just a
rotation of the first.
- Since they have the same shape and size, and one can be transformed into the other by rotation, they are congruent.
🔹
Answer:
Congruent because the triangles have the same shape and size; one is simply a rotation of the other.
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✔ Question 3)
Shapes: Two red L-shaped figures.
- The left shape is a small "L" made of three squares.
- The right shape is a larger "L" made of more squares.
- Visually, the
right shape is bigger than the left.
- Although both have an L-shape, they are
not the same size.
- So, they are
not congruent.
🔹
Answer:
Not congruent because the shapes are different sizes. The right shape is larger than the left one, so they cannot be identical in size and shape.
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✔ Final Answers:
| Question | Are they congruent? | Reason |
|--------|---------------------|--------|
| 1) | No | Different sizes — one is much larger than the other. |
| 2) | Yes | Same shape and size; one is a rotation of the other. |
| 3) | No | Different sizes — the second shape is larger. |
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✔ Summary:
- Congruence =
Same shape AND same size.
- Rotation, reflection, or translation does
not affect congruence.
- Scaling (making bigger or smaller) makes shapes
not congruent.
Let me know if you'd like this turned into a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of congruent shape worksheets.
