Classifying Quadrilaterals by mikao · Ninja Plans - Free Printable

Let's solve this step by step. The task is to classify each quadrilateral based on:

- Number of right angles
- Number of pairs of equal length sides
- Number of pairs of parallel sides
- Then, circle the correct words that describe the shape (from the list: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, TRAPEZOID, QUADRILATERAL)

We'll go through each figure one at a time.

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Figure 1: Rectangle

This is a rectangle (a box-like shape with four right angles).

- Right angles: 4 (all corners are 90°)
- Pairs of equal length sides: 2 pairs (opposite sides are equal)
- Pairs of parallel sides: 2 pairs (both pairs of opposite sides are parallel)
- Descriptive words to circle:
- ✔ RECTANGLE (it's a rectangle)
- ✔ PARALLELOGRAM (rectangles are parallelograms)
- ✔ QUADRILATERAL (all four-sided shapes are quadrilaterals)

> Note: It’s not a square unless all sides are equal (which they aren’t here), and it’s not a rhombus unless all sides are equal.

✔ Answer for Figure 1:
- Right angles: 4
- Equal length sides: 2 pairs
- Parallel sides: 2 pairs
- Circle: RECTANGLE, PARALLELOGRAM, QUADRILATERAL

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Figure 2: Rhombus (tilted diamond)

This is a rhombus — all sides are equal in length, but angles are not necessarily 90°.

- Right angles: 0 (unless specified, no right angles in a general rhombus)
- Pairs of equal length sides: 4 sides are equal → 2 pairs? Actually, better to say all 4 sides are equal, so 2 pairs of equal sides (but technically, there are two pairs of equal adjacent sides). However, since all sides are equal, we can say 2 pairs or just note "all 4 sides equal". But the question asks for pairs of equal length sides, so if all four are equal, then:
- You have two pairs of equal-length sides (e.g., side A = B, C = D, and also A = C, etc.), but actually, it's more accurate to say all four sides are equal, so 2 pairs (since a pair is two sides) — but actually, there are two pairs of opposite sides that are equal. Since all sides are equal, every side matches another.
- So: 2 pairs of equal length sides — but wait: you can form two pairs (like AB and CD, AD and BC), but since all are equal, it's more than two pairs. But the standard way to count "pairs" is how many distinct pairs of sides are equal. In a rhombus, all four sides are equal, so there are 2 pairs of opposite equal sides, but actually, every side is equal to every other. However, the question likely wants how many pairs of equal-length sides — meaning how many such pairs exist?

But typically, in these worksheets, "pairs of equal length sides" means how many distinct pairs of opposite sides are equal. In a rhombus, both pairs of opposite sides are equal, so 2 pairs.

Alternatively, if we think about it: 4 sides, all equal → number of equal-length pairs = 6 (each side matches 3 others), but that's not what is meant.

Standard interpretation: number of pairs of equal-length sides refers to how many pairs of sides are equal in length, grouped as pairs. Since all 4 sides are equal, there are 2 pairs of opposite equal sides.

Wait — actually, even better: in geometry, when asked "how many pairs of equal length sides", it usually means how many pairs of sides are equal. Since all 4 sides are equal, we can group them into 2 pairs (e.g., top and bottom, left and right), but really, all are equal.

But the answer expected is usually 2 pairs (since there are two sets of opposite sides, and both are equal).

So: 2 pairs of equal-length sides.

- Parallel sides: 2 pairs (both pairs of opposite sides are parallel)
- Right angles: 0 (no right angles in a typical rhombus unless it's a square)

- Descriptive words to circle:
- ✔ RHOMBUS (this is a rhombus)
- ✔ PARALLELOGRAM (rhombuses are parallelograms)
- ✔ QUADRILATERAL (all 4-sided shapes)

✘ Not a square, rectangle, or trapezoid.

✔ Answer for Figure 2:
- Right angles: 0
- Equal length sides: 2 pairs (all four sides are equal, but counted as 2 pairs of opposite sides)
- Parallel sides: 2 pairs
- Circle: RHOMBUS, PARALLELOGRAM, QUADRILATERAL

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Figure 3: Trapezoid (one pair of parallel sides)

This is a trapezoid — only one pair of parallel sides (the top and bottom bases).

- Right angles: 0 (unless specified, but here no indication of right angles)
- Equal length sides: Likely 0 pairs of equal-length sides (unless it's an isosceles trapezoid, but from the image, it appears not symmetric). So assume 0 pairs of equal-length sides
- Parallel sides: 1 pair (only top and bottom are parallel)
- Descriptive words to circle:
- ✔ TRAPEZOID
- ✔ QUADRILATERAL

✘ Not a square, rectangle, rhombus, or parallelogram (since only one pair of parallel sides)

✔ Answer for Figure 3:
- Right angles: 0
- Equal length sides: 0 pairs
- Parallel sides: 1 pair
- Circle: TRAPEZOID, QUADRILATERAL

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Figure 4: Square

This is a square — all sides equal, all angles 90°.

- Right angles: 4
- Equal length sides: All 4 sides are equal → 2 pairs of equal-length sides (or could say 4 sides equal, but again, counted as 2 pairs of opposite sides)
- Parallel sides: 2 pairs (both pairs of opposite sides are parallel)
- Descriptive words to circle:
- ✔ SQUARE
- ✔ RECTANGLE (squares are rectangles)
- ✔ RHOMBUS (squares are rhombuses)
- ✔ PARALLELOGRAM (squares are parallelograms)
- ✔ QUADRILATERAL

✔ Answer for Figure 4:
- Right angles: 4
- Equal length sides: 2 pairs (or more precisely, all sides equal, so 2 pairs)
- Parallel sides: 2 pairs
- Circle: SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL

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Figure 5: Parallelogram (slanted rectangle)

This is a parallelogram — opposite sides are parallel and equal, but angles are not 90°.

- Right angles: 0
- Equal length sides: 2 pairs (opposite sides are equal)
- Parallel sides: 2 pairs (both pairs of opposite sides are parallel)
- Descriptive words to circle:
- ✔ PARALLELOGRAM
- ✔ QUADRILATERAL

✘ Not a square, rectangle, or rhombus (unless specified — but here, sides are not all equal, and no right angles)

✔ Answer for Figure 5:
- Right angles: 0
- Equal length sides: 2 pairs
- Parallel sides: 2 pairs
- Circle: PARALLELOGRAM, QUADRILATERAL

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✔ Final Answers Table:

| FIGURE | Right Angles | Equal Length Pairs | Parallel Side Pairs | Words to Circle |
|--------|--------------|---------------------|----------------------|------------------|
| 1 (Rectangle) | 4 | 2 | 2 | RECTANGLE, PARALLELOGRAM, QUADRILATERAL |
| 2 (Rhombus) | 0 | 2 | 2 | RHOMBUS, PARALLELOGRAM, QUADRILATERAL |
| 3 (Trapezoid) | 0 | 0 | 1 | TRAPEZOID, QUADRILATERAL |
| 4 (Square) | 4 | 2 | 2 | SQUARE, RECTANGLE, RHOMBUS, PARALLELOGRAM, QUADRILATERAL |
| 5 (Parallelogram) | 0 | 2 | 2 | PARALLELOGRAM, QUADRILATERAL |

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🔍 Summary Notes:

- Quadrilateral: Any 4-sided polygon — all figures are quadrilaterals.
- Parallelogram: Opposite sides parallel and equal → includes rectangles, rhombuses, squares.
- Rectangle: 4 right angles + opposite sides equal and parallel.
- Rhombus: All sides equal, opposite sides parallel, no right angles (unless square).
- Square: Special case — all sides equal, all angles 90°.
- Trapezoid: Exactly one pair of parallel sides.

Let me know if you'd like this filled out in a printable format!