Classifying Quadrilaterals worksheet for students to identify properties of different quadrilateral shapes.

Let’s go step by step for each shape. We’ll count:

- Right angles (90-degree corners)
- Pairs of equal-length sides
- Pairs of parallel sides
- Then circle the correct name(s) from the list

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Shape 1: Rectangle (tall one)

- Right angles? → All 4 corners are right angles → 4
- Equal length sides? → Opposite sides are equal → 2 pairs (top-bottom, left-right) → 2 pairs
- Parallel sides? → Top || bottom, left || right → 2 pairs
- Names that fit: SQUARE? No — not all sides equal. RECTANGLE? Yes. RHOMBUS? No. PARALLELOGRAM? Yes (rectangles are parallelograms). TRAPEZOID? Some definitions say yes (at least one pair), but usually we pick more specific. QUADRILATERAL? Yes — it has 4 sides.

But since “RECTANGLE” is listed and fits best, and also “PARALLELOGRAM” and “QUADRILATERAL” technically fit, but in school worksheets like this, they often want the *most specific* answer. However, the instruction says “circle the word(s)” — plural — so we can circle multiple if they apply.

Actually, let’s check standard classification:

→ A rectangle is a type of parallelogram and quadrilateral. So all three apply. But sometimes teachers expect only the most specific. Let’s look at the options again.

Wait — the worksheet says “Circle the word(s) that describe(s)” — so if multiple apply, circle them.

But to be safe and accurate:

Rectangle = has 4 right angles, opposite sides equal and parallel → so it is also a parallelogram and quadrilateral.

So for Shape 1:
- Right angles: 4
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

BUT — wait! In many elementary curricula, they teach that a rectangle is NOT called a parallelogram unless specified, but mathematically it is. Since the worksheet includes both, and says “word(s)”, I think we should include all that truly describe it.

However, looking at common practice on such worksheets, they often expect just the most specific term. Let me double-check with Shape 4 (square) — which will help us see the pattern.

Actually, let’s do all shapes first, then decide.

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Shape 2: Parallelogram (slanted, no right angles)

- Right angles? → None → 0
- Equal length sides? → Opposite sides equal → 2 pairs → 2 pairs
- Parallel sides? → Both pairs of opposite sides parallel → 2 pairs
- Names: Not square, not rectangle, not rhombus (unless all sides equal — but drawing doesn’t show that), not trapezoid (if trapezoid means exactly one pair — but some define as at least one). Actually, this is a parallelogram → so circle PARALLELOGRAM and QUADRILATERAL.

Rhombus? Only if all 4 sides equal — drawing looks like opposite sides equal, adjacent may not be → so probably not rhombus.

Trapezoid? If defined as “exactly one pair of parallel sides”, then no. If “at least one”, then yes — but since it has two pairs, it’s better classified as parallelogram.

In most US elementary schools, trapezoid = exactly one pair. So we won’t circle trapezoid.

So for Shape 2:
- Right angles: 0
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: PARALLELOGRAM, QUADRILATERAL

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Shape 3: Trapezoid (one pair parallel, non-parallel sides slanting)

Assuming it’s an isosceles trapezoid (looks symmetric):

- Right angles? → None → 0
- Equal length sides? → The two non-parallel sides look equal → 1 pair → 1 pair
- Parallel sides? → Only top and bottom → 1 pair
- Names: TRAPEZOID (yes), QUADRILATERAL (yes). Not others.

Is it a parallelogram? No — only one pair parallel.

So:
- Right angles: 0
- Equal side pairs: 1
- Parallel side pairs: 1
- Circle: TRAPEZOID, QUADRILATERAL

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Shape 4: Square

- Right angles? → All 4 → 4
- Equal length sides? → All 4 sides equal → how many pairs? Well, you can pair them: side1=side2, side3=side4, etc. But typically, we say “pairs of equal length sides” meaning sets of two sides that are equal.

Since all four are equal, every side equals every other side. But in terms of distinct pairs, there are C(4,2)=6 pairs — but that’s not what they mean.

In context, they likely mean “how many pairs of sides are equal in length” — and since all sides are equal, you could say 2 pairs of opposite sides, or even 4 sides all equal → but standard way: in a square, there are 2 pairs of opposite sides that are equal (but actually all are equal).

Wait — let’s think: in a rectangle, we said 2 pairs (opposite sides). In a square, same thing — opposite sides are equal, but also adjacent sides are equal. But the question is “pairs of equal length sides”.

Perhaps they mean: how many sets of two sides have the same length.

In a square, all sides same → so any two sides form a pair of equal length. But that would be too many.

Looking back at Shape 1 (rectangle): we said 2 pairs — meaning the two pairs of opposite sides.

Similarly, for square, it’s the same: 2 pairs of opposite sides are equal — but actually, since all are equal, it’s still 2 pairs if we group opposite.

But actually, in a square, you can also say there are 4 sides all equal, so number of pairs of equal sides is higher — but I think for consistency with rectangle, we say 2 pairs (meaning the two sets of opposite sides).

Wait — no. Let’s clarify:

When we say “pairs of equal length sides”, in geometry worksheets, for a square, since all sides are equal, it’s common to say “all sides equal” or “4 equal sides”, but the question asks for “pairs”.

Perhaps they mean: how many pairs of sides are congruent.

In a square, every side is congruent to every other side, so there are 6 possible pairs — but that’s not practical.

I recall that in such contexts, for a square, they often say “2 pairs” same as rectangle, because they’re thinking of opposite sides.

But let’s check online or standard approach.

Actually, think: in a rhombus, all sides equal, so same issue.

Perhaps the intended meaning is: how many sets of two sides that are equal in length, considering the shape's properties.

For simplicity, and to match typical worksheet answers:

- Square: 4 right angles, 2 pairs of equal sides (opposite), 2 pairs of parallel sides.

But wait — in a square, adjacent sides are also equal, so why not more?

I think the convention is to count the number of pairs of sides that are equal, where a "pair" means two sides that are matched by the shape's symmetry.

Standard answer for square in such tables:
- Right angles: 4
- Pairs of equal sides: 2 (meaning the two pairs of opposite sides — even though all are equal, they still report 2 pairs like rectangle)
- Pairs of parallel sides: 2

And names: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL — because a square is all of those.

Yes! That makes sense. A square is a special rectangle, special rhombus, etc.

So for Shape 4 (square):
- Right angles: 4
- Equal side pairs: 2 (but actually, since all sides equal, some might say 4, but I think 2 is expected here for consistency)
Wait — let's think differently.

In a square, how many pairs of sides are equal? If we consider that each side is equal to the other three, but the question is "pairs", so perhaps it's the number of distinct pairs.

But to avoid confusion, let's look at the rhombus definition.

A rhombus has all sides equal, so same as square for side lengths.

In many sources, for a rhombus, they say "all sides equal" or "4 equal sides", but when asked for "pairs", it's ambiguous.

Perhaps the worksheet expects:

For square:
- Right angles: 4
- Pairs of equal length sides: 2 (referring to the two pairs of opposite sides, even though all are equal)
- Pairs of parallel sides: 2
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Similarly for rhombus later.

But let's confirm with Shape 5.

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Shape 5: Rhombus (diamond shape, all sides equal, no right angles)

- Right angles? → None → 0
- Equal length sides? → All 4 sides equal → so how many pairs? Again, if we say 2 pairs of opposite sides, but actually all are equal.
- Parallel sides? → Opposite sides parallel → 2 pairs
- Names: RHOMBUS, PARALLELOGRAM, QUADRILATERAL. Not square (no right angles), not rectangle.

For equal side pairs: since all sides equal, it's similar to square. Probably they expect 2 pairs, meaning the opposite sides are equal (which they are, and additionally adjacent are equal, but they might still say 2 pairs).

To resolve this, let's assume that "pairs of equal length sides" means the number of sets of two sides that are equal, and for shapes with all sides equal, it's still reported as 2 pairs for consistency with rectangles, or perhaps 4.

I found a better way: in some worksheets, for a square, they say "4 equal sides" but the question is "pairs", so perhaps it's the number of pairs you can make.

But let's calculate:

In a quadrilateral, there are 4 sides. Number of ways to choose 2 sides out of 4 is 6. But that's not helpful.

Perhaps they mean: how many pairs of sides are congruent, where a "pair" is a set of two sides that are equal, and they are counted based on the shape's properties.

For example, in a rectangle, there are two pairs: the two lengths are equal, the two widths are equal.

In a square, the two lengths are equal, the two widths are equal, but since length=width, it's the same.

So still 2 pairs.

In a rhombus, all sides equal, so the two pairs of opposite sides are equal, and also adjacent are equal, but typically, they still say 2 pairs for the opposite sides.

I think for this worksheet, we'll go with:

- For square and rhombus, "pairs of equal length sides" = 2, same as rectangle and parallelogram.

But let's verify with a reliable source in my mind.

Upon second thought, in a rhombus, since all sides are equal, you could argue there are more than 2 pairs, but in educational contexts, they often simplify.

Perhaps the intended answer is:

- Square: 4 right angles, 2 pairs of equal sides (opposite), 2 pairs parallel
- Rhombus: 0 right angles, 2 pairs of equal sides (opposite), 2 pairs parallel

But for rhombus, all sides are equal, so why not 4 pairs? I think it's safer to say 2 pairs, as the opposite sides are the pairs they're referring to.

Another idea: "pairs of equal length sides" might mean how many sets of two sides have the same length, and for a square, since all are same, it's 1 set of 4, but the question says "pairs", so perhaps it's the number of pairs within that.

I recall that in some curricula, for a square, they say "all sides equal" and don't specify pairs, but here they ask for pairs.

Let's look at the trapezoid: we said 1 pair for the non-parallel sides if isosceles.

For parallelogram, 2 pairs.

For rectangle, 2 pairs.

For square, logically, it should be 2 pairs as well, because the property is that opposite sides are equal, which is true, and additionally all are equal, but the basic property is 2 pairs.

Moreover, in the circle section, for square, we circle multiple names, including rhombus, which emphasizes that all sides are equal.

So for counting, we'll use:

- Square: 4 right angles, 2 pairs of equal sides, 2 pairs parallel
- Rhombus: 0 right angles, 2 pairs of equal sides, 2 pairs parallel

But for rhombus, if all sides are equal, then the number of pairs of equal sides is actually higher, but I think for this level, they expect 2.

Perhaps "pairs" means the number of side pairs that are equal, and in a rhombus, there are 2 pairs of opposite sides that are equal, and since all are equal, it's fine.

I think we should proceed with that.

So for Shape 5 (rhombus):
- Right angles: 0
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Now back to Shape 4 (square):
- Right angles: 4
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Yes.

Now let's summarize all:

Shape 1: Rectangle
- Right angles: 4
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

Shape 2: Parallelogram
- Right angles: 0
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: PARALLELOGRAM, QUADRILATERAL

Shape 3: Trapezoid
- Right angles: 0
- Equal side pairs: 1 (assuming isosceles, non-parallel sides equal)
- Parallel side pairs: 1
- Circle: TRAPEZOID, QUADRILATERAL

Shape 4: Square
- Right angles: 4
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Shape 5: Rhombus
- Right angles: 0
- Equal side pairs: 2
- Parallel side pairs: 2
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

But for Shape 3, is it isosceles? The drawing shows a trapezoid with non-parallel sides equal, so yes.

Also, for Shape 1, should we circle only RECTANGLE, or also others? Since the instruction says "word(s)", and mathematically it is also a parallelogram and quadrilateral, I think we should circle all that apply.

Similarly for others.

In some worksheets, they might expect only the most specific, but the problem says "circle the word(s)", implying possibly multiple.

To be precise, let's list all that correctly describe the shape.

Final decision:

For each shape, circle all names that accurately describe it based on its properties.

So:

- Rectangle: is a rectangle, parallelogram, quadrilateral → circle those three.
- Parallelogram: is a parallelogram, quadrilateral → circle those two.
- Trapezoid: is a trapezoid, quadrilateral → circle those two. (Assuming trapezoid means at least one pair parallel; if exactly one, then still trapezoid and quadrilateral.)
- Square: is a square, rectangle, rhombus, parallelogram, quadrilateral → circle all five.
- Rhombus: is a rhombus, parallelogram, quadrilateral → circle those three.

Now for the counts, we have:

Shape 1: 4, 2, 2
Shape 2: 0, 2, 2
Shape 3: 0, 1, 1
Shape 4: 4, 2, 2
Shape 5: 0, 2, 2

For Shape 3, equal side pairs: if it's isosceles trapezoid, the two legs are equal, so one pair of equal sides. The bases are not necessarily equal, so only one pair.

Yes.

So now, let's write the final answer as per the table.

Since the user wants the solution, I'll provide the completed table values.

Final Answer:

For each row:

Row 1 (Rectangle):
- How many right angles? 4
- How many pairs of equal length? 2
- How many pairs of parallel sides? 2
- Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

Row 2 (Parallelogram):
- How many right angles? 0
- How many pairs of equal length? 2
- How many pairs of parallel sides? 2
- Circle: PARALLELOGRAM, QUADRILATERAL

Row 3 (Trapezoid):
- How many right angles? 0
- How many pairs of equal length? 1
- How many pairs of parallel sides? 1
- Circle: TRAPEZOID, QUADRILATERAL

Row 4 (Square):
- How many right angles? 4
- How many pairs of equal length? 2
- How many pairs of parallel sides? 2
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Row 5 (Rhombus):
- How many right angles? 0
- How many pairs of equal length? 2
- How many pairs of parallel sides? 2
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Note: For "pairs of equal length sides", in squares and rhombuses, although all sides are equal, we report 2 pairs to be consistent with how rectangles and parallelograms are treated (i.e., counting the two pairs of opposite sides). This is standard in such worksheets.

Also, for the circling, we include all applicable terms as per mathematical definitions.

So the final answer is the filled-in table as above.