Congruent or similar Shapes Worksheet with Rainbow Border (black ... - Free Printable

Let’s go through each pair of shapes one by one and decide if they are congruent or similar.

Remember:
- Congruent means the shapes are exactly the same size AND shape. You can flip, turn, or slide them — but they must match perfectly.
- Similar means the shapes have the same shape but might be different sizes. Like a small photo and a big poster of the same picture.

---

Row 1: Two diamonds (rhombuses)
The first diamond is tall and skinny. The second is short and wide. They’re not the same shape — one is stretched differently. So they are not congruent, and also not similar because their angles or proportions are different. Wait — actually, let’s look again. Are they both rhombuses? Yes. But are they scaled versions? No — one is rotated and changed in proportion. Actually, looking closely, they appear to be the same shape but rotated — wait no, the side lengths seem different relative to height. Hmm… Actually, in most worksheets like this, if two shapes are the same type but different orientation or size, we check carefully.

Wait — let me re-express: In geometry, for polygons to be similar, corresponding angles must be equal and sides proportional. For congruent, all sides and angles must match exactly.

Looking at Row 1: First shape is a rhombus standing on its point (tall). Second is lying flat (wide). If you rotate the first one 90 degrees, does it match the second? Not quite — the aspect ratio looks different. Actually, upon closer inspection, these may be intended to be similar — same shape, different orientation/size? Or maybe not. Let’s compare with standard worksheet logic.

Actually, I think there’s a better way: Let’s assume that unless specified otherwise, if two shapes are the same type (e.g., both hearts, both squares) but different sizes, they are similar. If same size and shape, congruent.

But in Row 1: Both are rhombuses. Are they the same size? Visually, no — one is taller, one is wider. But are they proportional? Maybe not. This is tricky without measurements.

Wait — perhaps the worksheet expects us to judge visually.

Let me go row by row with visual judgment:

---

Row 1: Diamond vs Diamond (rotated)
They look like the same shape, just turned. If you rotate the first one, it matches the second? Actually, no — the first has longer vertical diagonal, second has longer horizontal. So unless it's a square (which it’s not), rotating changes the appearance. But mathematically, a rhombus rotated is still congruent if same side lengths. But here, do they have same side lengths? We can’t measure, but visually, they look like same size — just rotated. So probably congruent? Or maybe not.

This is confusing. Let’s try another approach.

In many elementary worksheets:

- If two shapes are identical in size and shape → Congruent
- If same shape but different size → Similar
- If different shape → Neither

So let’s apply that.

---

Row 1: Two rhombuses. One upright, one tilted. Do they look same size? Roughly yes. Same shape? Yes — both rhombuses. Since rotation doesn’t change congruence, they should be congruent.

But wait — sometimes worksheets consider orientation. No, congruence allows rotation.

I think Row 1 is Congruent.

---

Row 2: Two hearts
First heart is larger than the second. Same shape? Yes. Different size? Yes. So Similar.

---

Row 3: Square vs Rhombus
Square has 4 equal sides and 90-degree angles. Rhombus has 4 equal sides but angles not necessarily 90. Here, the rhombus is clearly not a square — it’s slanted. So different shapes. Therefore, neither congruent nor similar? But the options only give Congruent or Similar. Hmm.

Wait — is a square a type of rhombus? Yes, technically. But for similarity, angles must match. A square has all 90°, this rhombus does not. So not similar. And definitely not congruent. But since the worksheet forces a choice, perhaps it’s a trick.

Looking at the image: The square is axis-aligned, the other is a diamond shape — which could be a square rotated 45 degrees? Oh! Wait — if you rotate a square 45 degrees, it looks like a diamond. And if the side lengths are the same, then it’s congruent.

Are they the same size? Visually, the square and the diamond — if the diamond is a rotated square, then yes, congruent.

In fact, in many such worksheets, a square and a “diamond” that is actually a rotated square are considered congruent.

So Row 3: Congruent

---

Row 4: Spade vs Heart with stem
Spade symbol vs heart with a little triangle on top. Different shapes entirely. Not similar, not congruent. But again, forced choice. Probably neither, but since we must choose, likely neither — but options don’t have that. Wait, the worksheet says "Congruent or Similar?" implying one of them might be correct, or perhaps some are neither.

But looking at the format, each row has checkboxes for Congruent and Similar — so possibly both unchecked? But the instruction says "Enter Text here" — wait, no, the directions say "Enter Text here" but that might be placeholder.

Actually, re-reading: "Directions: Enter Text here" — that seems like a template error. Probably meant to say "Check the correct box".

Assuming we must choose one or leave blank, but for accuracy, let’s think.

Spade and heart-with-stem: very different shapes. Not similar. Not congruent. So perhaps no answer, but that might not be intended.

Maybe the heart-with-stem is meant to be a heart, and spade is different. I think this pair is neither, but since the problem likely expects an answer, and given common mistakes, perhaps it's a trick.

Another thought: In playing cards, spade and heart are different suits, so different shapes. Definitely not similar or congruent.

But let's see the next rows.

---

Row 5: Triangle pointing up vs triangle pointing down
Both are triangles. If they are equilateral or same type, and same size, then congruent even if flipped. Visually, they look same size and shape — just one inverted. So Congruent.

---

Row 6: Pentagon vs smaller pentagon
Same shape, different size. So Similar.

---

Now back to Row 4: Spade vs Heart-with-stem. The heart-with-stem might be intended as a heart, but it has a stem, while spade has a different base. Actually, comparing: spade has a rounded top with a point at bottom and a stem; the other has a heart shape with a small triangle on top — like an apple or something. Very different. So not similar, not congruent. But perhaps in the context, it's a mistake, or perhaps we should say neither. However, since the worksheet provides only those two options, and for consistency, maybe it's designed to be "neither", but that might not be selectable.

Perhaps I misidentified. Let me describe:

Left: spade symbol — like ♠

Right: heart with a small triangle on top — like ♥ with a hat, or an apple.

Definitely different shapes. So not similar, not congruent. But since the problem asks to choose between congruent or similar, and if neither applies, perhaps leave blank, but the user expects answers.

Maybe for Row 4, it's neither, but let's see what makes sense.

Another idea: perhaps the right one is meant to be a heart, and left is spade, so different, so no. But in some fonts, they might look similar, but here they don't.

I think for accuracy, Row 4 is neither, but since the format might expect an answer, and to avoid overcomplicating, let's look for patterns.

Perhaps all pairs are either congruent or similar except this one. But let's count.

Maybe the heart-with-stem is actually a heart, and the stem is part of it, but still different from spade.

I recall that in some worksheets, such pairs are used to show non-similar shapes.

But to proceed, I'll assume that for Row 4, since shapes are fundamentally different, it's not similar or congruent, but perhaps the intended answer is "neither", but since not an option, maybe the worksheet has a flaw. However, for the sake of completing, let's say it's not applicable, but that's not helpful.

Wait — perhaps "similar" means same general shape, but no, in math, similar has specific meaning.

Let's search my knowledge: in geometry education, for young students, "similar" often means same shape different size, "congruent" same size and shape.

For Row 4, shapes are different, so neither.

But let's check online or standard practice. Since I can't, I'll make a decision.

Perhaps the right shape is a heart, and left is spade, so different, so no checkbox. But the user might expect us to select based on visual.

Another thought: maybe the heart-with-stem is meant to be compared as a heart, and spade is different, so not similar.

I think I should go with:

Row 1: Congruent (same rhombus, rotated)

Row 2: Similar (hearts, different sizes)

Row 3: Congruent (square and rotated square)

Row 4: Neither — but since must choose, perhaps it's a trick, and they are not similar, so leave blank, but for the answer, I'll say not congruent or similar, but that's not possible.

Perhaps in this context, "similar" is loosely used, but I doubt it.

Let's look at the last two rows for clue.

Row 5: Triangles, same size, flipped — congruent

Row 6: Pentagons, different sizes — similar

So for Row 4, if I have to choose, I'd say neither, but since the problem likely intends for us to identify when they are congruent or similar, and this pair is neither, perhaps it's ok to not select, but the final answer needs to be provided.

Maybe the heart-with-stem is actually a spade variant, but no.

I recall that in some symbols, the spade and heart are both curved, but here the right one has a straight-sided triangle on top, while spade has curved sides.

So different.

Perhaps the intended answer for Row 4 is "neither", but since the format doesn't allow, and to move forward, I'll assume that for this pair, it's not congruent or similar, so no selection, but for the sake of the exercise, let's see what the majority would be.

Another idea: perhaps "similar" means they look alike, but in math, it's precise.

I think I made a mistake earlier. Let's redefine with clear criteria.

For each pair:

1. Are the shapes identical in size and shape (allowing rotation/reflection)? -> Congruent

2. Are the shapes the same shape but different size (proportional)? -> Similar

3. Otherwise -> Neither

Apply:

Row 1: Two rhombuses. If they have the same side lengths and angles, then congruent even if rotated. Visually, they appear to be the same size — the first is taller, but that might be due to orientation. In a rhombus, rotating it doesn't change its dimensions. So if the side lengths are equal, they are congruent. I think they are intended to be congruent. So Congruent

Row 2: Hearts, different sizes, same shape -> Similar

Row 3: Square and diamond. If the diamond is a square rotated 45 degrees, and same side length, then congruent. Visually, the square and the diamond have the same "width" if measured, but the diamond's diagonal is longer. Actually, for a square of side s, when rotated 45 degrees, the bounding box is larger, but the shape itself is the same. In terms of the figure, if the side lengths are equal, it's congruent. Here, the square has sides parallel to axes, the diamond has vertices at top,bottom,left,right. If the distance from center to vertex is the same, then for a square, the diagonal is s√2, while for the diamond oriented that way, if it's a square, the side length would be the same. I think it's safe to assume they are congruent. So Congruent

Row 4: Spade and heart-with-stem. Spade has a specific shape: two curves meeting at a point at bottom, with a stem. The other has a heart shape (two curves meeting at bottom) with a triangle on top. So the overall shape is different — one has a pointed bottom, the other has a rounded bottom with a flat-top triangle. So not the same shape. Therefore, neither congruent nor similar. But since the worksheet may expect an answer, and perhaps in this context, it's considered not similar, so no checkbox, but for the final answer, I'll note it as neither.

However, to comply with the format, perhaps the intended answer is that they are not congruent or similar, so for this row, no selection, but that might not be satisfactory.

Maybe the heart-with-stem is meant to be a heart, and spade is different, so not similar.

I think for accuracy, I'll say for Row 4, it is neither, but since the problem asks to solve, and to provide final answer, perhaps list the choices.

Perhaps in some interpretations, they are both "card suit-like", but that's not mathematical.

Let's skip and come back.

Row 5: Two triangles, same size, one upright, one inverted. If they are equilateral or isosceles with same dimensions, then congruent. Visually, they look identical in size and shape, just flipped. So Congruent

Row 6: Two pentagons, same shape, different sizes. So Similar

Now for Row 4, after careful thought, I believe the shapes are different, so not congruent or similar. But perhaps the worksheet has a typo, or perhaps the right shape is meant to be a heart without stem, but it has a stem.

Looking back at the image description: "spade" and "heart with a small triangle on top" — so likely, the heart-with-stem is not a standard heart, but a modified shape.

So I think it's neither.

But to provide an answer, and since the user might expect selections, I'll assume that for Row 4, it is not congruent or similar, so no box checked, but for the final answer format, I need to state for each row.

Perhaps the "Final Answer" should be a list of choices for each row.

Let me define the answers as per my best judgment:

Row 1: Congruent

Row 2: Similar

Row 3: Congruent

Row 4: Neither (but since not an option, perhaps leave blank, but for the sake of completion, I'll say not applicable, but that's not good)

Another idea: perhaps "similar" includes same type, but no.

I recall that in some curricula, for young students, they might consider the spade and heart as both "curvy shapes", but that's not accurate.

Perhaps the heart-with-stem is actually a spade in some fonts, but here it's drawn differently.

I think I should go with:

For Row 4, since the shapes are fundamentally different, it is neither congruent nor similar. But since the worksheet likely intends for us to identify when they are one or the other, and this pair is an exception, perhaps it's ok.

To resolve, let's assume that the heart-with-stem is meant to be a heart, and spade is different, so not similar, and not congruent, so for this row, no selection. But for the final answer, I'll include it as "neither" in text.

But the response format requires a final answer, so perhaps list the choices.

Perhaps the "Final Answer" is the selection for each row.

Let me write the answers as:

1. Congruent

2. Similar

3. Congruent

4. Neither

5. Congruent

6. Similar

But "Neither" is not an option in the checkboxes, so perhaps for Row 4, it's left blank, but in the context, maybe the teacher expects "similar" if they look somewhat alike, but I doubt it.

Let's look for a different approach. Perhaps in Row 4, the spade and the heart-with-stem are both symmetric and have a stem, but the body is different.

I think I'm overcomplicating. Let's use common sense for elementary level.

In many such worksheets, if two shapes are the same type (e.g., both triangles, both circles), they are similar if different size, congruent if same size. If different types, neither.

Here, spade and heart are different types of symbols, so neither.

So for the final answer, I'll state for each row what it is.

Perhaps the "Final Answer" section should be a list.

Let's do that.

After careful analysis:

- Row 1: The two diamonds are the same size and shape, just rotated. So Congruent.

- Row 2: The two hearts are the same shape but different sizes. So Similar.

- Row 3: The square and the diamond are the same size and shape; the diamond is a rotated square. So Congruent.

- Row 4: The spade and the heart-with-stem are different shapes. So Neither congruent nor similar. (But since the worksheet may not have that option, in practice, no box is checked, but for this response, I'll note it.)

- Row 5: The two triangles are the same size and shape, just flipped. So Congruent.

- Row 6: The two pentagons are the same shape but different sizes. So Similar.

For Row 4, to fit the format, perhaps the intended answer is that they are not similar, so no selection, but I think for accuracy, I'll include "neither" in the explanation.

Since the user said "solve the problem accurately", I'll be accurate.

So for the final answer, I'll provide the correct classification for each row.

Final Answer:
Row 1: Congruent
Row 2: Similar
Row 3: Congruent
Row 4: Neither
Row 5: Congruent
Row 6: Similar

But "Neither" might not be expected, so perhaps in some contexts, they consider it similar if both are "heart-like", but the spade is not heart-like.

Upon second thought, the heart-with-stem might be intended as a heart, and the spade is different, so not similar.

I think it's fine.

Perhaps the worksheet has a mistake, but for now, I'll go with that.

So to box the answer.

The final answer should be the selections.

Since the response format says "provide only the final correct answer", and it's multiple parts, I'll list them.

So:

Final Answer:
1. Congruent
2. Similar
3. Congruent
4. Neither
5. Congruent
6. Similar

But to match the worksheet, perhaps specify for each.

Since the user might expect the choices, and for Row 4, if must choose, I'd say not applicable, but I think "Neither" is honest.

Another idea: in the image, the heart-with-stem might be a misdrawn heart, but it has a triangle on top, while spade has a different base.

I recall that in some symbols, the spade is like an upside-down heart with a stem, but here the right one has a heart shape with a triangle on top, which is different.

So I stand by "Neither" for Row 4.

So for the final answer.