Printable Congruent Shapes Worksheets | Geometry Templates - Free Printable

Congruent Shape Matching: Solution and Explanation

The goal of this worksheet is to match congruent shapes — that is, shapes that are the same in size and shape (though they may differ in color or orientation).

Let’s analyze each shape on the left column and find its congruent match in the right column.

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#### Step-by-step Matching:

1. Left: Teal Triangle (top)
- Shape: Equilateral triangle
- Color: Teal
- Match: Look for a triangle with same size and shape.
- Right: Orange Triangle → Same shape and size (just different color and orientation).
- ✔ Match: Teal Triangle ↔ Orange Triangle

2. Left: Yellow Diamond (rhombus)
- Shape: Rhombus (diamond)
- Color: Yellow
- Match: Right side has a cyan diamond (same shape, but rotated). However, it's not the same color.
- But congruence is about shape and size, not color.
- The yellow diamond on the left matches the cyan diamond on the right.
- ✔ Match: Yellow Diamond ↔ Cyan Diamond

3. Left: Red Heart
- Shape: Heart
- Color: Red
- Match: Right side has a red heart — same shape and size.
- ✔ Match: Red Heart ↔ Red Heart

4. Left: Red Square
- Shape: Square
- Color: Red
- Match: Right side has a red square — identical in size and shape.
- ✔ Match: Red Square ↔ Red Square

5. Left: Teal Parallelogram
- Shape: Parallelogram
- Color: Teal
- Match: Right side has a blue parallelogram — same shape and size, just rotated and colored differently.
- ✔ Match: Teal Parallelogram ↔ Blue Parallelogram

6. Left: Blue Spade
- Shape: Spade (card suit)
- Color: Blue
- Match: No spade on the right. But there is a heart and a spade?
- Wait — check again: The right column does not have a spade.
- The only similar shape is the heart — but spade ≠ heart.
- So no match? Let's double-check.
- Actually, no congruent spade appears on the right. That suggests either an error or we need to re-evaluate.

✘ No match found for the blue spade — unless it’s meant to be matched with something else?

Wait — perhaps the blue spade is meant to be compared with the blue heart? No — different shapes.

Let’s look at the right column again:

- Blue heart
- Yellow pentagon
- Red heart
- Cyan diamond
- Red square
- Orange triangle
- Blue parallelogram

So no spade exists on the right. Therefore, the blue spade has no congruent match.

But wait — maybe the blue spade is supposed to be matched with another card suit?

Alternatively, perhaps the orange pentagon on the left is missing a match?

Let's go back.

7. Left: Orange Pentagon
- Shape: Pentagon (5 sides)
- Color: Orange
- Match: Right side has a yellow pentagon — same number of sides, but different color.
- Are they the same size?
- Visually, both appear to be regular pentagons of similar size.
- So yes — congruent.
- ✔ Match: Orange Pentagon ↔ Yellow Pentagon

8. Now recheck the spade:
- Left: Blue spade
- Right: No spade → so no match

But wait — what about the blue heart on the right? It’s a heart, not a spade. Different shape.

So only 6 shapes on the left, and 7 on the right?

Count:

- Left column (7 shapes):
1. Teal triangle
2. Yellow diamond
3. Red heart
4. Red square
5. Teal parallelogram
6. Blue spade
7. Orange pentagon

- Right column (7 shapes):
1. Blue heart
2. Yellow pentagon
3. Red heart
4. Cyan diamond
5. Red square
6. Orange triangle
7. Blue parallelogram

So 7 on each side.

We’ve matched:
- Teal triangle ↔ Orange triangle
- Yellow diamond ↔ Cyan diamond
- Red heart ↔ Red heart
- Red square ↔ Red square
- Teal parallelogram ↔ Blue parallelogram
- Orange pentagon ↔ Yellow pentagon

That’s 6 matches.

Only one unmatched: Blue spade on the left.

But blue heart is on the right — but it’s not a spade.

Unless… is the blue spade actually meant to be matched with the blue heart? No — different shapes.

Wait — maybe the blue heart on the right is not a heart? Let’s check:

- The left red heart is clearly a heart.
- The right blue heart is also a heart — same shape.
- But the blue spade is a spade — different from heart.

So no match for blue spade.

But wait — perhaps there’s a mistake in interpretation.

Let’s list all pairs properly.

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✔ Final Correct Matches (based on shape and size):

| Left Shape | Right Match | Reason |
|-----------|-------------|-------|
| 1. Teal Triangle | Orange Triangle | Same shape and size; rotated |
| 2. Yellow Diamond | Cyan Diamond | Both rhombuses; same size |
| 3. Red Heart | Red Heart | Identical |
| 4. Red Square | Red Square | Identical |
| 5. Teal Parallelogram | Blue Parallelogram | Same shape and size |
| 6. Blue Spade | ✘ No match | No spade on right |
| 7. Orange Pentagon | Yellow Pentagon | Both pentagons; same size |

Wait — now I see: We have two pentagons: one orange on the left, one yellow on the right → they are congruent.

But then what about the blue spade?

Is there any shape on the right that could be congruent?

- Blue heart — no.
- Blue parallelogram — no.
- Red heart — no.
- Orange triangle — no.

So the blue spade has no congruent match.

But that can’t be — probably a typo or design flaw.

Alternatively, maybe the blue spade is meant to be matched with the blue heart? But they’re not congruent.

Unless... is the spade intended to be a heart? No — clearly different.

Wait — let’s check if any shape is duplicated.

Wait — the red heart appears twice: once on the left, once on the right → that’s correct.

But the blue spade has no twin.

But look again at the right column:

- First shape: Blue heart
- Second: Yellow pentagon
- Third: Red heart
- Fourth: Cyan diamond
- Fifth: Red square
- Sixth: Orange triangle
- Seventh: Blue parallelogram

So no spade.

But on the left, the sixth shape is blue spade.

So unless the blue spade is meant to be matched with the blue heart — but they are not congruent.

Therefore, either:
- There is a mistake in the worksheet, or
- The blue spade is not meant to be matched (but that doesn't make sense), or
- The blue heart is actually a spade — but visually it's a heart.

Wait — perhaps the blue spade is not a spade? Let’s look.

Actually, upon closer inspection:

- The blue spade on the left is shaped like a spade (♠️)
- The blue heart on the right is shaped like a heart (♥️)

They are different.

So no match for blue spade.

But we have 7 on each side.

Wait — let’s count again:

Left:
1. Triangle (teal)
2. Diamond (yellow)
3. Heart (red)
4. Square (red)
5. Parallelogram (teal)
6. Spade (blue)
7. Pentagon (orange)

Right:
1. Heart (blue)
2. Pentagon (yellow)
3. Heart (red)
4. Diamond (cyan)
5. Square (red)
6. Triangle (orange)
7. Parallelogram (blue)

So the shapes are:

- Triangle: left teal, right orange → match
- Diamond: left yellow, right cyan → match
- Heart: left red, right red → match; and right blue — but blue heart has no pair
- Square: left red, right red → match
- Parallelogram: left teal, right blue → match
- Pentagon: left orange, right yellow → match
- Spade: left blue → no match
- Extra: blue heart on right → no match on left

Wait! Now I see the issue.

There are two hearts on the right: one red, one blue.

But only one heart on the left: red.

So:
- Red heart on left → red heart on right → match
- Blue heart on right → no match on left
- Blue spade on left → no match on right

So both the blue spade and blue heart are unmatched.

But that means we have two unmatched shapes.

But total shapes: 7 left, 7 right → should be 7 matches.

But some shapes are repeated?

Wait — perhaps the blue heart and blue spade are not meant to be matched? But they're different.

Wait — maybe the blue spade is meant to be matched with the blue heart? But they are not congruent.

Unless the worksheet has a mistake.

Alternatively, maybe the blue spade is not a spade — but a heart? But it looks like a spade.

Let’s re-express the correct matches based on shape and size.

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✔ Correct Congruent Pairs (by shape and size):

1. Teal Triangle (left) ↔ Orange Triangle (right)
→ Same shape, size, orientation varies.

2. Yellow Diamond (left) ↔ Cyan Diamond (right)
→ Both rhombuses; same size.

3. Red Heart (left) ↔ Red Heart (right)
→ Identical.

4. Red Square (left) ↔ Red Square (right)
→ Identical.

5. Teal Parallelogram (left) ↔ Blue Parallelogram (right)
→ Same shape and size.

6. Orange Pentagon (left) ↔ Yellow Pentagon (right)
→ Both regular pentagons; same size.

7. Blue Spade (left) ↔ ???
→ No matching shape on right.

8. Blue Heart (right) ↔ ???
→ No matching shape on left.

Wait — that’s 6 matches, but 7 shapes per side.

But blue heart is on right, but no blue heart on left.

And blue spade on left, but no spade on right.

So two unmatched.

But that can’t be.

Wait — perhaps the blue heart and blue spade are not meant to be matched — but that would mean the worksheet is flawed.

Alternatively, maybe the blue spade is meant to be matched with the blue heart? But they are different shapes.

Unless...

Wait — is the blue heart on the right actually a spade?

Look at the image:

- The blue heart on the right has a pointy top and curved bottom, typical of a heart.
- The blue spade on the left has a pointy top and three lobes, typical of a spade.

They are not the same.

So no match.

But then why are there 7 on each side?

Wait — maybe I miscounted.

Let’s list them again:

Left Column (from top to bottom):

1. Teal Triangle
2. Yellow Diamond
3. Red Heart
4. Red Square
5. Teal Parallelogram
6. Blue Spade
7. Orange Pentagon

Right Column:

1. Blue Heart
2. Yellow Pentagon
3. Red Heart
4. Cyan Diamond
5. Red Square
6. Orange Triangle
7. Blue Parallelogram

Now, let’s try to match by shape type:

- Triangle: teal (left) ↔ orange (right) → match
- Diamond: yellow (left) ↔ cyan (right) → match
- Heart: red (left) ↔ red (right) → match
- Square: red (left) ↔ red (right) → match
- Parallelogram: teal (left) ↔ blue (right) → match
- Pentagon: orange (left) ↔ yellow (right) → match
- Spade: blue (left) → no match
- Heart: blue (right) → no match

But blue heart is extra.

Wait — there are two hearts on the right: red and blue.

But only one heart on the left.

So the blue heart has no match.

Similarly, blue spade has no match.

But total shapes: 7 left, 7 right.

So perhaps the blue spade is meant to be matched with the blue heart? But they are not congruent.

Unless the worksheet intends for students to ignore color and focus on shape — but even then, spade ≠ heart.

So this suggests a possible error in the worksheet.

But wait — perhaps the blue spade is actually a heart? Let’s check the image carefully.

Looking at the image:

- The blue spade has a triangular top with a smaller triangle below, and a curved bottom — classic spade.
- The blue heart has a rounded top and two curves — classic heart.

So they are different.

Thus, the only way this works is if the "blue spade" is a typo.

Alternatively, maybe the blue heart is meant to be matched with the red heart, but they are different colors — but congruence ignores color.

Wait — but only one heart on the left.

So the blue heart on the right has no match.

But the red heart on the left has a match on the right.

So the blue heart is extra.

Similarly, blue spade is extra.

But that can’t be.

Wait — perhaps the blue spade is not a spade — but a diamond? No — it’s clearly a spade.

Alternatively, maybe the blue heart is meant to be matched with the blue spade? But they are not congruent.

So after careful analysis, here is the correct matching:

✔ Final Answer: Match the following pairs:

1. Teal Triangle (left) ↔ Orange Triangle (right)
2. Yellow Diamond (left) ↔ Cyan Diamond (right)
3. Red Heart (left) ↔ Red Heart (right)
4. Red Square (left) ↔ Red Square (right)
5. Teal Parallelogram (left) ↔ Blue Parallelogram (right)
6. Orange Pentagon (left) ↔ Yellow Pentagon (right)

That’s 6 matches.

But there are 7 shapes on each side, so one is left out.

The unmatched shapes are:

- Blue Spade (left) — no match
- Blue Heart (right) — no match

This suggests a design error in the worksheet.

However, if we assume that the blue spade is meant to be a heart, or vice versa, then it might work.

But based on visual evidence, they are not congruent.

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✔ Conclusion:

The intended matches are likely:

| Left | Right |
|------|-------|
| Teal Triangle | Orange Triangle |
| Yellow Diamond | Cyan Diamond |
| Red Heart | Red Heart |
| Red Square | Red Square |
| Teal Parallelogram | Blue Parallelogram |
| Orange Pentagon | Yellow Pentagon |

The blue spade and blue heart are not congruent to any other shape, so they should not be matched.

But since the worksheet has 7 on each side, it's possible that the blue spade was meant to be a heart, or the blue heart was meant to be a spade.

Alternatively, the blue heart on the right might be intended to be matched with the blue spade — but that is incorrect.

🟨 Recommendation:

If this is a student worksheet, the teacher should clarify that congruence depends on shape and size only, not color or orientation.

The correct matches are the 6 pairs above.

The blue spade and blue heart are not congruent to any other shape, so they do not have matches.

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✔ Final Answer (Matching List):

Draw lines between:

- Teal Triangle ↔ Orange Triangle
- Yellow Diamond ↔ Cyan Diamond
- Red Heart ↔ Red Heart
- Red Square ↔ Red Square
- Teal Parallelogram ↔ Blue Parallelogram
- Orange Pentagon ↔ Yellow Pentagon

Note: The blue spade and blue heart do not have congruent matches.