Rectangles, rhombuses and squares · Grade 9
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
For example: In the rectangle ABCD the diagonals meet at O . The diagonal AC is 40 cm. How long is BO ?
Answer and solution
The answer: 20 cm
BD = AC = 40 BO = 40 ÷ 2 = 20
Diagonals of a rhombus
For example: 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 and solution
The answer: 10 cm
AO = 12 ÷ 2 = 6 BO = 16 ÷ 2 = 8 AB² = 6² + 8² = 36 + 64 = 100 AB = 10
Properties of a square
For example: The diagonal of a square is 20 cm. What is the area of the square?
Answer and solution
The answer: 200 cm²
20 × 20 ÷ 2 = 200
The median to the hypotenuse
For example: 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 and solution
The answer: 4 cm
BM = 8 ÷ 2 = 4
Which quadrilateral is it?
For example: In the quadrilateral ABCD the diagonals are equal and bisect each other. Which quadrilateral is it for certain? Choose the most precise name.
- Square
- Rhombus
- Rectangle
- Parallelogram
Answer and solution
The answer: Rectangle
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
Parts of this topic that are not built 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, so there are new exercises every time. The topic follows the Israeli Ministry of Education's grade 9 maths curriculum (2026–27).