# Rectangles, rhombuses and squares · Grade 9

> Rectangles, rhombuses and squares, Grade 9: Diagonals of a rectangle and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Rectangles, rhombuses and squares (Grade 9) you practise 5 skills: Diagonals of a rectangle · Diagonals of a rhombus · Properties of a square · The median to the hypotenuse · Which quadrilateral is it?.

A rectangle is a parallelogram with a right angle, so all its angles are right angles. Its diagonals are equal and bisect each other. In a right triangle the median to the hypotenuse is half the hypotenuse: it is half a diagonal of the rectangle that the triangle is half of.

A rhombus is a parallelogram with all sides equal. Its diagonals are perpendicular, bisect each other and bisect the angles. The area of a rhombus is half the product of its diagonals.

A square is both a rectangle and a rhombus, so it has every property of both. To decide which quadrilateral you have, choose the most precise name the givens guarantee.

**Tip:** Every property of a parallelogram also holds in a rectangle, a rhombus and a square.

## What you learn

### Diagonals of a rectangle

- Example: (A rectangle with its two diagonals dashed, meeting at a point.) In the rectangle ABCD the diagonals meet at O . The diagonal AC is 40 cm. How long is BO ?
- Answer: 20 cm
- Solution: BD = AC = 40 BO = 40 ÷ 2 = 20

### Diagonals of a rhombus

- Example: (A rhombus with its two diagonals dashed, meeting at a point.) In the rhombus ABCD the diagonals meet at O . Given AC = 12, BD = 16 (in cm). How long is a side of the rhombus?
- Answer: 10 cm
- Solution: AO = 12 ÷ 2 = 6 BO = 16 ÷ 2 = 8 AB² = 6² + 8² = 36 + 64 = 100 AB = 10

### Properties of a square

- Example: (A square with its two diagonals dashed, meeting at a point.) The diagonal of a square is 20 cm. What is the area of the square?
- Answer: 200 cm²
- Solution: 20 × 20 ÷ 2 = 200

### The median to the hypotenuse

- Example: (A right triangle with the median to the hypotenuse, dashed.) In the triangle ABC has ∢B = 90° , and BM is the median to the hypotenuse AC . The hypotenuse is 8 cm. How long is the median?
- Answer: 4 cm
- Solution: BM = 8 ÷ 2 = 4

### Which quadrilateral is it?

- Example: In the quadrilateral ABCD the diagonals are equal and bisect each other. Which quadrilateral is it for certain? Choose the most precise name.
- Options: Square · Rhombus · Rectangle · Parallelogram
- Answer: Rectangle
- Solution: A quadrilateral whose diagonals bisect each other is a parallelogram. A parallelogram with equal diagonals is a rectangle. The diagonals are not given as perpendicular, so you cannot say it is a square. The answer: rectangle.

## Not on the site yet

- Proving that a quadrilateral is a rectangle, a rhombus or a square
- Proving that the median to the hypotenuse is half of it

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education's grade 9 maths curriculum (2026–27).

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