Classifying Quadrilaterals by mikao · Ninja Plans - Free Printable

Let’s go through each shape one by one. We’ll count:

- How many right angles (90-degree corners)?
- How many pairs of equal-length sides?
- How many pairs of parallel sides?
- Then circle the correct name(s) from the list.

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Shape 1: Rectangle (tall and skinny)

- Right angles: All 4 corners are right angles → 4
- Equal length sides: Opposite sides are equal → top = bottom, left = right → 2 pairs
- Parallel sides: Top ∥ bottom, left ∥ right → 2 pairs
- Names that fit: It’s a rectangle, also a parallelogram, and always a quadrilateral. Not a square (sides not all equal), not a rhombus (not all sides equal), not a trapezoid (has two pairs of parallel sides).

→ Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

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Shape 2: Parallelogram (slanted, no right angles)

- Right angles: None → 0
- Equal length sides: Opposite sides equal → 2 pairs
- Parallel sides: Both pairs opposite sides are parallel → 2 pairs
- Names: It’s a parallelogram and quadrilateral. Not a rectangle (no right angles), not a rhombus (unless all sides equal — this one doesn’t look like it), not a square or trapezoid.

→ Circle: PARALLELOGRAM, QUADRILATERAL

*(Note: If it were a rhombus, all 4 sides would be equal — but in this drawing, it looks like only opposite sides are equal, so we’ll assume it’s just a general parallelogram.)*

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Shape 3: Trapezoid (one pair of parallel sides, slanted sides)

- Right angles: None → 0
- Equal length sides: The non-parallel sides might be equal? In this drawing, they look equal — so maybe 1 pair? But actually, in a standard trapezoid like this, unless marked, we don’t assume. Let’s check: top and bottom are different lengths, left and right look same length → so 1 pair of equal sides? Wait — actually, in many curricula, if it’s an isosceles trapezoid, the legs are equal. This looks like one. So let’s say 1 pair.
- Parallel sides: Only top and bottom are parallel → 1 pair
- Names: Definitely a trapezoid and quadrilateral. Not others.

→ Circle: TRAPEZOID, QUADRILATERAL

*(Some definitions say trapezoid has exactly one pair of parallel sides — which fits here.)*

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Shape 4: Square

- Right angles: All 4 → 4
- Equal length sides: All 4 sides equal → that’s 2 pairs? Wait — actually, if all 4 are equal, you can think of it as 2 pairs (top-bottom, left-right), but technically, every side equals every other side. However, the question says “pairs of equal length sides” — so how many *pairs*? Since all 4 are equal, any two form a pair — but usually, we count distinct matching pairs. Standard answer for square: 2 pairs of equal sides? No — wait, better way: in a square, there are 4 sides, all equal. So number of pairs of equal-length sides: since all are equal, you could say 6 possible pairs, but that’s not what’s meant. Actually, in geometry worksheets like this, they mean “how many sets of two sides that are equal”. For a square, opposite sides are equal (that’s 2 pairs), AND adjacent sides are also equal — but typically, they expect: since all sides are equal, it has 2 pairs of equal sides? That doesn’t make sense.

Wait — let’s rethink.

Actually, in most elementary contexts, when they say “pairs of equal length sides”, they mean how many pairs of sides that are congruent to each other.

In a square:
- Side A = Side B = Side C = Side D
So, you can pair them as:
- Pair 1: Top & Bottom
- Pair 2: Left & Right
But also, Top = Left, etc. — but that’s overcounting.

Standard approach in such worksheets: for a square, since all sides are equal, it has 2 pairs of equal sides? No — actually, I recall now: in a square, there are 4 sides, all equal, so the number of "pairs" is often considered as 2 (opposite pairs), but that’s misleading.

Better: Think of it as — how many sets of two sides that have the same length. Since all four are same, any two form a pair — but again, not practical.

Looking at common answers for such problems:

For a square:
- Right angles: 4
- Pairs of equal sides: 2? Or 4? Wait — no.

Actually, let’s look at the rhombus vs square.

Perhaps the intended meaning is: how many pairs of sides that are equal in length, counting each unique pair once.

But to avoid confusion, let’s use standard textbook answers.

In a square:
- All 4 sides equal → so number of pairs of equal-length sides: since all are equal, it's more than 2. But in practice, for classification, they often say a square has 2 pairs of equal sides? That doesn't sound right.

I think I made a mistake.

Let me clarify with definitions used in elementary math:

- A square has 4 equal sides → so it has 2 pairs of parallel sides, 4 right angles, and for "pairs of equal length sides", since all sides are equal, it has multiple pairs, but typically, they might expect "2" if they mean opposite pairs, but that’s incorrect because adjacent sides are also equal.

Actually, upon second thought, in many curriculum materials, for a square, they say:

- Number of pairs of equal sides: 2 (meaning two sets of opposite sides are equal — but since all are equal, it's redundant).

This is confusing.

Alternative approach: perhaps "pairs of equal length sides" means how many pairs of sides that are congruent, and for a square, since all sides are congruent, the number of such pairs is C(4,2)=6, but that’s absurd for this level.

I recall now: in such worksheets, for a square, they usually put 2 for pairs of equal sides? No.

Let’s think differently. Look at the rhombus: a rhombus has 4 equal sides, so same issue.

Perhaps the question means: how many pairs of sides that are equal, where a "pair" is two sides that match, and they want the count of such matching groups.

But for simplicity, in most cases:

- Square: 4 right angles, 2 pairs of parallel sides, and for equal sides — since all 4 are equal, it has 2 pairs? I think I need to check a reliable source mentally.

Actually, I remember: in some texts, they say a square has 2 pairs of equal sides — but that’s wrong because all sides are equal.

Perhaps they mean "number of sets of two sides that are equal", and for a square, you can say there are 2 pairs if you consider only opposite, but that’s not accurate.

Let’s look at the first shape: rectangle. We said 2 pairs of equal sides — which is correct: top=bottom, left=right.

For a square, similarly, top=bottom, left=right, and also top=left, etc., but the minimal answer is still 2 pairs if we consider the opposite pairs.

But in reality, a square has more symmetry.

To resolve this, let's assume that "pairs of equal length sides" means the number of pairs of sides that are congruent, and for a polygon, it's common to report the number of distinct pairs based on grouping.

For a square, since all sides are equal, it has 4 sides of equal length, so the number of "pairs" isn't straightforward.

I found a better way: in many online resources for similar worksheets, for a square, they put:

- Right angles: 4
- Pairs of equal sides: 2 (but that must be a mistake)

No, let's think: in a square, there are 4 sides. The number of ways to choose 2 sides that are equal: since all are equal, every pair is equal, but that's not helpful.

Perhaps the question intends: how many pairs of sides that are equal in length, meaning how many sets of two sides that have the same length, and for a square, since all are same, it's infinite, but that's silly.

I recall now: in some contexts, "pairs of equal sides" means the number of pairs of opposite sides that are equal. For both rectangle and square, that's 2 pairs.

For a rhombus, also 2 pairs of opposite sides equal, but since all sides are equal, it's the same.

For the purpose of this worksheet, I believe they expect:

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

Similarly for rhombus.

Let's proceed with that convention, as it's consistent with the rectangle.

So for Shape 4: Square

- Right angles: 4
- Pairs of equal length sides: 2 (top-bottom, left-right)
- Pairs of parallel sides: 2
- Names: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL — because a square is all of these.

Yes, a square is a special type of rectangle, rhombus, parallelogram, and quadrilateral.

So circle all except trapezoid.

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

- Right angles: 0
- Equal length sides: All 4 sides equal → so again, how many pairs? Same issue. By convention, we'll say 2 pairs of equal sides (opposite), but actually all are equal. To be consistent, let's say 2 pairs for now.
- Parallel sides: 2 pairs (opposite sides parallel)
- Names: RHOMBUS, PARALLELOGRAM, QUADRILATERAL. Not square (no right angles), not rectangle, not trapezoid.

→ Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

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Now, let's tabulate everything clearly.

Final Answers per Row:

Row 1 (Rectangle):
- Right angles: 4
- Pairs of equal length sides: 2
- Pairs of parallel sides: 2
- Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

Row 2 (Parallelogram):
- Right angles: 0
- Pairs of equal length sides: 2
- Pairs of parallel sides: 2
- Circle: PARALLELOGRAM, QUADRILATERAL

Row 3 (Trapezoid):
- Right angles: 0
- Pairs of equal length sides: 1 (the two non-parallel sides are equal — assuming isosceles trapezoid)
- Pairs of parallel sides: 1
- Circle: TRAPEZOID, QUADRILATERAL

Row 4 (Square):
- Right angles: 4
- Pairs of equal length sides: 2 (by convention, though all sides equal)
- Pairs of parallel sides: 2
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Row 5 (Rhombus):
- Right angles: 0
- Pairs of equal length sides: 2 (again, by convention)
- Pairs of parallel sides: 2
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

Wait, for the rhombus, if all sides are equal, should "pairs of equal length sides" be more than 2? But in the context of this worksheet, since they ask for "pairs", and for consistency with rectangle, I think 2 is expected.

To confirm, let's think about what "pairs" means. If a shape has 4 sides all equal, then there are multiple pairs, but typically in such tables, they might expect the number of pairs of opposite sides that are equal, which is 2 for both rhombus and square.

I think it's safe to go with that.

Also, for the trapezoid, if it's isosceles, the legs are equal, so 1 pair of equal sides.

Now, writing the final answer as requested.

Final Answer:
For each row, fill in the blanks as follows:

Row 1 (first figure - 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 (second figure - 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 (third figure - 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 (fourth figure - 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 (fifth figure - rhombus):
- How many right angles? 0
- How many pairs of equal length? 2
- How many pairs of parallel sides? 2
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL