Properties of Quadrilaterals quiz with multiple-choice questions on geometry concepts.

Here's the solution to the Properties of Quadrilaterals quiz, with clear explanations for each question:

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1. The interior angle sum of a quadrilateral is...

✔ Answer: A) 360

Explanation:
Any quadrilateral (4-sided polygon) can be divided into two triangles. Since each triangle has an interior angle sum of 180°, the total is 2 × 180° = 360°.

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2. The diagonals of a ________ are perpendicular.

✔ Answer: C) Rhombus

Explanation:
In a rhombus, the diagonals always intersect at right angles (perpendicular). This is one of its defining properties.
- Rectangles: diagonals are congruent but not necessarily perpendicular (unless it’s a square).
- Trapezoids: diagonals are generally not perpendicular.
- Parallelograms: diagonals bisect each other but are not perpendicular unless it’s a rhombus or square.

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3. All squares are rectangles

✔ Answer: B) True

Explanation:
A square is a special type of rectangle — it has all the properties of a rectangle (four right angles, opposite sides equal and parallel) plus additional properties (all sides equal, diagonals perpendicular). So yes, all squares are rectangles, but not all rectangles are squares.

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4. If a parallelogram is a rhombus, then the diagonals are congruent.

✔ Answer: A) False

Explanation:
In a rhombus (which is a type of parallelogram), the diagonals are perpendicular and bisect each other, but they are not necessarily congruent.
- Diagonals are congruent only in rectangles and squares.
So, this statement is false.

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5. A ________ is a quadrilateral with exactly one pair of parallel sides.

✔ Answer: B) Trapezoid

Explanation:
By definition, a trapezoid has exactly one pair of parallel sides (called the bases).
- Kite: no requirement for parallel sides.
- Rhombus/Parallelogram: have two pairs of parallel sides.

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6. Each diagonal of a ________ bisects a pair of opposite angles.

✔ Answer: D) Rhombus

Explanation:
In a rhombus, each diagonal bisects the angles at the vertices it connects. This is a key property.
- Rectangle: diagonals do not bisect angles (unless it’s a square).
- Parallelogram: diagonals don’t necessarily bisect angles.
- Trapezoid: diagonals don’t have this property.

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7. If a quadrilateral is both a rhombus and a rectangle, then it is a square.

✔ Answer: B) True

Explanation:
- A rhombus has all sides equal.
- A rectangle has all angles equal to 90°.
If a quadrilateral has all sides equal AND all angles 90°, then it must be a square.
So yes, this is true.

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8. Both pairs of base angles in an ________ are congruent.

✔ Answer: C) Isosceles Trapezoid

> *(Note: The image cuts off after “an ________”, but based on standard curriculum and context, the intended answer is Isosceles Trapezoid.)*

Explanation:
In an isosceles trapezoid, the non-parallel sides (legs) are congruent, and as a result, each pair of base angles (angles adjacent to the same base) are congruent.
This is a defining property of isosceles trapezoids.

*(Note: The options listed in the image are cut off — but if “Isosceles Trapezoid” was an option, that’s the correct choice. If only general trapezoid is listed, it would be misleading — because only *isosceles* trapezoids have congruent base angles.)*

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## ✔ Final Answers Summary:

| Question | Answer |
|----------|--------|
| 1 | A |
| 2 | C |
| 3 | B |
| 4 | A |
| 5 | B |
| 6 | D |
| 7 | B |
| 8 | C (Isosceles Trapezoid) *(assuming it’s an option)* |

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Let me know if you’d like help with questions 9 and 10 — they’re cut off in the image!