Quadrilateral worksheet with definitions, examples, and questions for students to identify and describe properties of quadrilaterals.

Let’s go step by step to answer each question based on the definitions given at the top of the worksheet.

We are told:

- A quadrilateral = closed figure with 4 sides.
- A parallelogram = quadrilateral where opposite sides are parallel and congruent.
- A rectangle = parallelogram with 4 right angles.
- A rhombus = parallelogram with 4 congruent sides.
- A square = has right angles AND 4 congruent sides → so it’s both a rectangle and a rhombus.
- A trapezoid = quadrilateral with only 1 pair of parallel sides.

Now let’s answer each question:

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1. Which quadrilateral have four right angles?

From definition:
→ Rectangle has 4 right angles.
→ Square also has 4 right angles (since it’s a special rectangle).

✔ So: Rectangle, Square

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2. Which quadrilateral has four congruent sides?

From definition:
→ Rhombus has 4 congruent sides.
→ Square also has 4 congruent sides (it’s a special rhombus).

✔ So: Rhombus, Square

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3. Are all rectangles also parallelograms?

Definition says: “A rectangle is a parallelogram with 4 right angles.”
That means every rectangle *is* a type of parallelogram — just one that also has right angles.

✔ Yes

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4. Are all squares also parallelograms?

Square has 4 right angles and 4 congruent sides → which means its opposite sides are parallel (because it’s a rectangle and a rhombus, both of which are parallelograms).

Also, since square is a special case of rectangle and rhombus, and those are parallelograms → yes.

✔ Yes

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5. Are all rectangles also rhombuses?

Rectangle: 4 right angles, opposite sides equal.
Rhombus: 4 congruent sides.

Not all rectangles have 4 congruent sides — only if it’s a square. For example, a long skinny rectangle does NOT have all sides equal.

So: No, not all rectangles are rhombuses.

✔ No

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6. Are all trapezoids also squares?

Trapezoid: only 1 pair of parallel sides.
Square: 2 pairs of parallel sides, 4 right angles, 4 congruent sides.

They’re very different! Trapezoid doesn’t even require right angles or equal sides.

✔ No

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7. Is a square also a rhombus?

Yes! Definition: Rhombus = 4 congruent sides. Square has that. Also, square is a special kind of rhombus that also has right angles.

✔ Yes

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Now for identifying shapes #8–11:

We need to match each shape to correct terms from the list: Parallelogram, Trapezoid, Rectangle, Rhombus, Square.

But note: Some shapes may fit more than one category. We should use ALL that apply.

Let’s analyze each:

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#8: Looks like a diamond tilted — all sides look equal, no right angles shown → this is a Rhombus.
Is it a parallelogram? Yes — because rhombus is a type of parallelogram.
Is it a square? No — no right angles visible.
Is it a rectangle? No.
Is it a trapezoid? No — it has 2 pairs of parallel sides.

✔ So: Parallelogram, Rhombus

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#9: Diamond shape but looks like it might have right angles? Wait — actually, in standard worksheets, if it’s drawn as a perfect diamond with equal sides and right angles, it’s a square. But here, looking closely — it’s rotated, but still appears to have 4 equal sides and 4 right angles → so it’s a Square.

And since square is also: rectangle, rhombus, parallelogram.

✔ So: Parallelogram, Rectangle, Rhombus, Square

Wait — let me double-check. In many textbooks, when they draw a square rotated 45 degrees, it’s still called a square. And since it has 4 right angles and 4 equal sides, yes.

But sometimes students get confused. Let’s stick to properties:

If all sides equal + all angles 90° → square → which implies it’s also rectangle, rhombus, parallelogram.

✔ So: Parallelogram, Rectangle, Rhombus, Square

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#10: Long horizontal shape — opposite sides equal and parallel, angles look like 90° → this is a Rectangle.

Which makes it also a Parallelogram.

Not a rhombus (sides not all equal), not a square, not a trapezoid.

✔ So: Parallelogram, Rectangle

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#11: Only one pair of parallel sides (top and bottom) → this is a Trapezoid.

No other categories fit — not parallelogram (needs 2 pairs), etc.

✔ So: Trapezoid

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Final Answers Summary:

1. Rectangle, Square
2. Rhombus, Square
3. Yes
4. Yes
5. No
6. No
7. Yes
8. Parallelogram, Rhombus
9. Parallelogram, Rectangle, Rhombus, Square
10. Parallelogram, Rectangle
11. Trapezoid

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Final Answer:
1. Rectangle, Square
2. Rhombus, Square
3. Yes
4. Yes
5. No
6. No
7. Yes
8. Parallelogram, Rhombus
9. Parallelogram, Rectangle, Rhombus, Square
10. Parallelogram, Rectangle
11. Trapezoid