Congruent shapes worksheet for identifying matching geometric figures.

Let's solve the "Congruent Shapes" worksheet step by step. The goal is to identify congruent shapes — shapes that are the same size and shape, even if they are rotated or flipped.

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🔹 Understanding Congruent Shapes

Two shapes are congruent if:
- They have the same shape
- They have the same size
- One can be transformed into the other via rotation, reflection, or translation (but not resizing)

We’ll go through each question.

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## ✔ Question 4: Which of the following shapes are congruent? Find two pairs and list the letters.

Look at the grid with labeled shapes A–J.

Let’s analyze each shape:

- A: Red square
- B: Yellow L-shaped (like a tetromino)
- C: Green diamond (rhombus)
- D: Purple triangle (right triangle)
- E: Pink rectangle
- F: Blue triangle (scalene?)
- G: Light blue triangle
- H: Orange square
- I: Yellow triangle
- J: Purple triangle

Now compare:

🔸 Pair 1: Look for identical squares

- A and H are both squares.
- But A is red, H is orange — but color doesn’t matter.
- Are they the same size?
- A is a 2x2 square (covers 4 unit squares).
- H is also a 2x2 square → yes!
✔ A and H are congruent.

🔸 Pair 2: Look for triangles

- D is a right triangle (purple), small.
- G is light blue, also a right triangle.
- Check sizes:
- D has legs of 1 and 2 units → area = 1
- G: same dimensions → yes
✔ D and G are congruent.

Wait — let’s check others too.

But look at I and F:
- I is yellow triangle — appears to be right triangle with legs 1 and 2 → same as D and G?
- But F is blue triangle — looks like it has different proportions?

Actually, D, G, and I all appear to be right triangles with legs 1 and 2.

Wait — let's double-check:

- D: purple triangle, base=2, height=1 → right triangle
- G: light blue triangle, same orientation → same size → congruent to D
- I: yellow triangle — appears same → maybe congruent too?

But the question says find two pairs.

So possible pairs:
- A and H (both 2×2 squares)
- D and G (both right triangles, 1×2 legs)
- Also, I might be congruent to D/G?

But I is in a different orientation — rotated.

Yes, I is a right triangle with legs 1 and 2 — same as D and G.

So actually, D, G, and I are all congruent.

But we need two pairs.

Let’s pick:
- A and H (squares)
- D and G (triangles)

✔ So answer: A and H, D and G

> ✔️ Answer for Question 4:
> A and H, D and G

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## ✔ Question 5: Which of the following shapes are congruent? List all that apply.

Now we have more shapes: A–L

Let’s go one by one.

Step 1: Identify types

- A: pink triangle
- B: yellow triangle
- C: green triangle
- D: red triangle
- E: yellow triangle (smaller)
- F: pink triangle
- G: green triangle
- H: yellow triangle
- I: red triangle
- J: pink triangle
- K: yellow triangle
- L: green triangle

Wait — many are triangles.

But also:

- M: red triangle (wait — no M, up to L)

Let’s label them properly.

Looking at the image:

Shapes:
- A: pink right triangle
- B: yellow right triangle (larger)
- C: green right triangle
- D: red right triangle
- E: yellow triangle (smaller, acute?)
- F: pink triangle (same as A?)
- G: green triangle (same as C?)
- H: yellow triangle (same as B?)
- I: red triangle (same as D?)
- J: pink triangle (same as A/F?)
- K: yellow triangle (same as E?)
- L: green triangle (same as C/G?)

Now compare:

🔸 Triangles of same type:

#### 🔹 Right triangles (legs 1 and 2):

- A: pink, right triangle
- F: pink, same shape and size → congruent
- J: pink, same → congruent

So A, F, J are all congruent (same size, shape, color doesn't matter).

✔ A, F, J are congruent

#### 🔹 Larger yellow right triangle:

- B: yellow, larger right triangle
- H: yellow, same shape and size → congruent
- K: yellow, smaller — no

Wait: B and H both look like right triangles with legs 2 and 3?

Check:
- B: base 3, height 2 → area = 3
- H: same → yes

So B and H are congruent.

✔ B and H

#### 🔹 Green right triangles:

- C: green right triangle (legs 1 and 2)
- G: green, same → congruent
- L: green, same → congruent

So C, G, L are congruent.

✔ C, G, L

#### 🔹 Red triangles:

- D: red right triangle (legs 1 and 2)
- I: red, same → congruent

✔ D and I

#### 🔹 Small yellow triangle (E and K):

- E: yellow, small triangle — appears equilateral or acute?
- K: yellow, same shape and size → congruent

But are they same as others? No — different from right triangles.

So E and K are congruent.

✔ E and K

Wait — are there any non-triangles?

No — all seem to be triangles.

But wait — E and K look like equilateral or acute triangles — not right triangles.

So they are a separate group.

Also, B and H are large right triangles.

Now let’s list all congruent groups:

| Group | Shapes |
|------|--------|
| 1 | A, F, J (pink right triangles) |
| 2 | B, H (yellow large right triangles) |
| 3 | C, G, L (green right triangles) |
| 4 | D, I (red right triangles) |
| 5 | E, K (small yellow acute triangles) |

But wait — E and K are the only ones in their group.

Now, are B and H really congruent?

Yes — same shape and size.

Similarly, C, G, L — same.

So now, list all that apply — meaning list all sets of congruent shapes.

But the instruction says: “List all that apply” — probably means list all pairs or groups that are congruent.

But since some have 3, we should list all pairs within groups.

But the format likely wants: list the letters of shapes that are congruent.

So best to list each group.

But the question says: “List all that apply.” — so perhaps write all congruent pairs or groups.

But looking at the space, probably list the letters of congruent shapes.

So final answer:

- A, F, J are congruent
- B, H are congruent
- C, G, L are congruent
- D, I are congruent
- E, K are congruent

But note: E and K are the same — small yellow triangle.

✔ So answer for Question 5:

> A, F, J; B, H; C, G, L; D, I; E, K

(Write them in boxes or list them clearly.)

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## ✔ Question 6: Which of the following shapes are congruent? List all that apply.

Now shapes A–L again, but different layout.

Let’s analyze.

Shapes:

- A: pink triangle
- B: yellow triangle
- C: green triangle
- D: red triangle
- E: yellow triangle
- F: pink triangle
- G: green triangle
- H: yellow triangle
- I: red triangle
- J: pink triangle
- K: yellow triangle
- L: green triangle

Again, mostly triangles.

Let’s find congruent ones.

🔸 Look for identical triangles

#### 🔹 Pink triangles (A, F, J):
- All appear to be right triangles with legs 1 and 2
- Same size and shape → congruent

✔ A, F, J

#### 🔹 Yellow triangles:
- B: yellow right triangle (large)
- E: yellow triangle — smaller?
- H: yellow triangle — looks same as B?
- K: yellow triangle — small?

Wait:

- B: yellow, right triangle, legs 2 and 3
- H: yellow, same — yes → congruent to B
- E: yellow, small — appears equilateral?
- K: yellow, same as E?

But E and K are small yellow triangles — same shape → congruent

So:
- B and H — large yellow right triangles
- E and K — small yellow triangles

But E and K — are they congruent?

Yes — same size and shape.

Now C, G, L — green triangles?

- C: green right triangle (legs 1 and 2)
- G: green, same → congruent
- L: green, same → congruent

So C, G, L

Red triangles:
- D: red right triangle (legs 1 and 2)
- I: red, same → congruent

So D and I

Now pink:
- A, F, J — already noted

Wait — F is pink, but in this image, is F same as A?

Yes — same shape and size.

So again:

Groups:
- A, F, J — pink right triangles
- B, H — large yellow right triangles
- C, G, L — green right triangles
- D, I — red right triangles
- E, K — small yellow acute triangles

Same as before!

But wait — is E and K really the same?

In this image, E and K are both small yellow triangles, pointing down, same size → yes.

So same pattern.

Therefore, answer is same as Question 5.

But wait — are E and K in the same group?

Yes.

So Question 6 answer is same as Question 5.

But let’s confirm.

Wait — in Question 6, shape E is a small yellow triangle, K is also small yellow triangle — same.

And B and H are large yellow right triangles.

So yes.

Thus:

✔ Answer for Question 6:

> A, F, J; B, H; C, G, L; D, I; E, K

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🟩 Final Answers:

#### Question 4:
> A and H, D and G

#### Question 5:
> A, F, J; B, H; C, G, L; D, I; E, K

#### Question 6:
> A, F, J; B, H; C, G, L; D, I; E, K

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✔ Explanation Summary:

- Congruent shapes must be same size and shape, regardless of rotation or position.
- We compared shapes by type, size, and proportions.
- Used visual inspection of grids to match side lengths and angles.
- Grouped shapes with matching properties (e.g., right triangles with legs 1 and 2).

Let me know if you'd like this formatted as a printable answer sheet!