Equal Parts of a Whole or Not? worksheet - Free Printable

Let’s go through each shape one by one and check if it is divided into equal parts.

We are looking for shapes where:
- The whole shape is split into parts.
- All parts are the same size and shape (or at least same area — in simple terms, they look identical or mirror images that fit perfectly).

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1. Circle split vertically down the middle → two equal halves → ✔ YES

2. Circle split with a diagonal line not through center → parts are unequal → ✘ NO

3. Square split diagonally → two triangles of equal size → ✔ YES

4. Rectangle split into 4 vertical strips → all same width → ✔ YES

5. Parallelogram split diagonally → two triangles, but since it’s a parallelogram, they are congruent → ✔ YES

Wait — actually, let’s double-check #5. In a parallelogram, a diagonal divides it into two congruent triangles — so yes, equal area and shape → ✔ YES

6. Heart split vertically down the middle → symmetric → two equal halves → ✔ YES

7. Diamond (rhombus) split horizontally → top and bottom triangles — are they equal? Yes, because it’s symmetric across horizontal axis → ✔ YES

Actually, wait — looking again: the diamond is split horizontally through the middle. Since it’s a rhombus (all sides equal), and split along the horizontal diagonal, the two triangles should be congruent → ✔ YES

But hold on — in some cases, if it’s not a square diamond, splitting horizontally might not give equal areas? No — in any rhombus, both diagonals bisect each other at right angles, and each diagonal splits the rhombus into two congruent triangles. So yes → ✔ YES

8. Circle split into 3 parts from center → like a peace sign → all three sectors look equal → ✔ YES

9. Diamond split vertically → left and right triangles — since it’s symmetric vertically → ✔ YES

10. Triangle split vertically down the middle → assuming it’s an isosceles triangle (which it looks like), then yes, two equal halves → ✔ YES

But wait — is it necessarily isosceles? In the diagram, it appears symmetric. We’ll assume based on visual symmetry → ✔ YES

11. Rectangle split into 4 vertical strips → all same width → ✔ YES

12. Heart split diagonally → not symmetric that way → parts are unequal → ✘ NO

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Now let’s list the ones that are divided into equal parts:

✔ 1, 3, 4, 5, 6, 7, 8, 9, 10, 11

✘ 2, 12

Wait — let me recheck #5 and #7 and #10 carefully.

#5: Parallelogram split by diagonal → always gives two congruent triangles → equal → ✔

#7: Rhombus split horizontally → if it's split along the shorter diagonal, still gives two congruent triangles → ✔

#10: Triangle split vertically — only equal if it’s isosceles. In the image, it looks like an isosceles triangle (symmetric), so we accept it → ✔

But what about #3? Square split diagonally → two equal right triangles → ✔

#8: Circle into 3 equal sectors → looks like 120 degrees each → ✔

So final list of correct answers: 1, 3, 4, 5, 6, 7, 8, 9, 10, 11

That’s 10 shapes.

But let me count again to be sure:

1. ✔
2. ✘
3. ✔
4. ✔
5. ✔
6. ✔
7. ✔
8. ✔
9. ✔
10. ✔
11. ✔
12. ✘

Yes — 10 correct.

Final Answer:
1, 3, 4, 5, 6, 7, 8, 9, 10, 11