Worksheet illustrating the properties of various geometric shapes with definitions and visual examples.

Let’s go step by step through each shape and check which properties apply. We’ll use the example (Rectangle) as a guide: for Rectangle, they checked “all 4 sides” (meaning all 4 angles are 90°? Wait — actually looking at the rectangle example, it says:

> Example: Rectangle
> ☑ all 4 sides → probably means “all 4 angles are 90°”? But wait, that doesn’t match. Let me re-read.

Actually, looking again — in the Rectangle box, it says:

- all 4 sides → but that can’t be right because rectangles don’t have all 4 sides equal. Oh! Wait — maybe it’s mislabeled? Or perhaps “all 4 sides” is meant to mean something else?

Wait — let’s look carefully at the example given for Rectangle:

It has three checkboxes:

1. ☑ all 4 sides → this must be a mistake? Because rectangles do NOT have all 4 sides equal. Squares do.

But then it also has:

2. ☑ two pairs of opposite sides are parallel → correct for rectangle.

3. ☐ diagonals bisect each other → not checked? But they should be!

Hmm — maybe the example is incomplete or there’s a typo? Actually, looking at the image description again — the user said “Example: Rectangle” and then listed:

- all 4 sides → this is likely an error in the worksheet. Rectangles do NOT have all 4 sides equal. Only squares do.

Wait — perhaps “all 4 sides” is meant to say “all 4 angles are 90°”? That would make sense. But the text says “all 4 sides”.

Alternatively, maybe it’s a formatting issue. Let me reinterpret based on standard geometry knowledge.

Actually, let’s ignore the example for now and focus on solving each shape correctly using real math facts.

We’ll go one by one.

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Right Triangle

Properties listed:

- sum of angles = 180° → ✔ TRUE for ALL triangles.
- one angle measures 90° → ✔ TRUE — that’s what makes it a *right* triangle.
- two sides are congruent → ✘ NOT necessarily true. Only if it’s also isosceles. A right triangle can have all sides different (like 3-4-5). So we leave this unchecked unless specified.

So for Right Triangle:
☑ sum of angles = 180°
☑ one angle measures 90°
two sides are congruent

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Square

Properties:

- all four angles = 90° → ✔ YES
- 4 sides same length → ✔ YES
- 2 pairs of opposite sides are parallel → ✔ YES (actually, both pairs are parallel — so yes)
- diagonals bisect each other → ✔ YES — in fact, they bisect at 90° and are equal.

Wait — the square section only lists 3 boxes? Looking back:

In the image description, under Square:

- ☑ all four angles = 90°
- ☑ 4 sides same length
- ☑ 2 pairs of opposite sides are parallel

That’s all? Diagonals aren’t mentioned here? But in Rhombus and others, diagonals are mentioned. Maybe for Square, they didn’t include diagonal property? Or maybe it’s implied?

Actually, looking at the original problem layout — each shape has its own set of checkboxes. For Square, only those 3 are listed? Then we check all 3.

But wait — in the Rectangle example, they had “diagonals bisect each other” as an option but didn’t check it? That seems odd.

Perhaps the worksheet is designed such that you only check what’s listed per shape.

So for Square, since all 3 listed properties are true, we check all 3.

But let’s confirm:

Square:
- All angles 90° → yes
- 4 sides same length → yes
- 2 pairs of opposite sides parallel → yes (in fact, both pairs are parallel)

✔ All three should be checked.

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Parallelogram

Properties listed:

- opposite sides are congruent → ✔ YES — definition of parallelogram
- diagonals bisect each other → ✔ YES — always true for parallelograms
- both pairs of opposite sides are parallel → ✔ YES — that’s the definition

Wait — the list says:

- ☐ opposite sides are congruent
- ☐ diagonals bisect each other
- ☐ both pairs of opposite sides are parallel

All three are TRUE for any parallelogram.

So we check all three.

But note: sometimes people confuse “both pairs” with just “one pair” — but no, parallelogram requires BOTH pairs of opposite sides to be parallel.

So:

Parallelogram:
☑ opposite sides are congruent
diagonals bisect each other
☑ both pairs of opposite sides are parallel

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Equilateral Triangle

Properties:

- all sides are the same length → ✔ YES — that’s the definition
- all angles are 60° → ✔ YES — because 180° / 3 = 60°
- all angles are 90° → ✘ NO — that’s impossible for a triangle. Sum would be 270°.

So:

Equilateral Triangle:
☑ all sides are the same length
☑ all angles are 60°
☐ all angles are 90°

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Rhombus

Properties:

- 4 sides are congruent → ✔ YES — definition of rhombus
- only two sides are congruent → ✘ NO — all four are
- diagonals are perpendicular → ✔ YES — key property of rhombus
- diagonals bisect each other → ✔ YES — also true

Wait — the list says:

- 4 sides are congruent
- ☐ only two sides are congruent
- ☐ diagonals are perpendicular
- ☐ diagonals bisect each other

So we check:

4 sides are congruent
☐ only two sides are congruent → false, skip
☑ diagonals are perpendicular
☑ diagonals bisect each other

Note: “only two sides are congruent” is wrong — rhombus has all four equal. So we leave that unchecked.

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Scalene Triangle

Properties:

- all sides are congruent → NO — scalene means NO sides equal
- only two sides are congruent → ✘ NO — that’s isosceles
- all sides are the same length → ✘ same as first — no
- all angles are 60° → ✘ no — that’s equilateral

Wait — the list says:

- ☐ all sides are congruent
- ☐ only two sides are congruent
- ☐ all sides are the same length → redundant with first? Probably typo, but still false
- ☐ all angles are 60° → false

Actually, scalene triangle has:

- All sides DIFFERENT lengths
- All angles DIFFERENT measures

None of the listed properties are true for scalene triangle? That can’t be right — maybe I’m missing something.

Looking again at the Scalene Triangle section:

The properties listed are:

- ☐ all sides are congruent → false
- only two sides are congruent → false
- all sides are the same length → false (same as first)
- ☐ all angles are 60° → false

Wait — that suggests none should be checked? But that seems odd. Perhaps there’s a mistake in the worksheet? Or maybe I misread.

Actually, let me double-check the original problem statement.

User wrote:

> Scalene Triangle
> all sides are congruent
> ☐ only two sides are congruent
> ☐ all sides are the same length
> ☐ all angles are 60°

Yes — all of these are FALSE for a scalene triangle.

But that would mean no boxes are checked? Is that possible?

In some worksheets, they might expect you to realize that none apply — but typically, they’d include at least one true property.

Wait — perhaps “all sides are the same length” is meant to be “no sides are the same length”? But it’s written as “all sides are the same length”, which is false.

Alternatively, maybe it’s a trick question — but for educational purposes, we must go by definitions.

Scalene triangle: no sides equal, no angles equal.

So none of the listed properties are true.

Therefore, for Scalene Triangle, we check NONE.

But let’s verify with standard knowledge:

- Scalene: all sides different → so “all sides congruent” = false, “only two congruent” = false, “all sides same length” = false, “all angles 60°” = false.

Yes — so no checks.

However, this feels unusual for a worksheet. Maybe there’s a typo? But since we must solve based on what’s given, we proceed.

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Now, let’s compile the answers clearly.

Final Answer format should list each shape and which boxes to check.

Since the user wants the final answer after reasoning, and ExplainAnswer is false, we just output the final checked boxes per shape.

But how to format? Probably like the example: for each shape, list the checked properties.

Since the original uses checkboxes, we can indicate which ones are checked.

Let me write it out:

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Right Triangle
☑ sum of angles = 180°
☑ one angle measures 90°
☐ two sides are congruent

Square
☑ all four angles = 90°
☑ 4 sides same length
☑ 2 pairs of opposite sides are parallel

Parallelogram
☑ opposite sides are congruent
☑ diagonals bisect each other
☑ both pairs of opposite sides are parallel

Equilateral Triangle
☑ all sides are the same length
☑ all angles are 60°
☐ all angles are 90°

Rhombus
☑ 4 sides are congruent
☐ only two sides are congruent
☑ diagonals are perpendicular
☑ diagonals bisect each other

Scalene Triangle
☐ all sides are congruent
☐ only two sides are congruent
☐ all sides are the same length
all angles are 60°

(Note: For Scalene Triangle, none of the properties listed are true, so all remain unchecked.)

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This matches geometric definitions.

I’ve verified each against standard properties.

No calculations needed beyond basic geometry facts.

Final Answer below.