A diagonal divides a convex quadrilateral into two triangles, so its interior angles total 360. Classify a quadrilateral from given properties; a tilted square remains a square. **Figure** | **Defining and useful properties** Parallelogram | Both pairs of opposite sides parallel; opposite sides and angles equal; diagonals bisect each other. Rectangle | A parallelogram with four right angles; diagonals are equal. Rhombus | A parallelogram with four equal sides; diagonals are perpendicular and bisect its angles. Square | Both a rectangle and a rhombus; it has all their properties. Trapezium | One pair of opposite sides parallel. An isosceles trapezium also has equal non-parallel sides and equal base angles. Kite | Two pairs of adjacent equal sides; its symmetry diagonal bisects the other diagonal at right angles. The opposite angles between unequal sides are equal. Example In parallelogram ABCD, A=72. Then C=72, and B= D=108. If its diagonals meet at M and AC=14 cm, then AM=7 cm. A general kite does not have two diagonals that bisect each other. Equal diagonals alone do not prove that a quadrilateral is a rectangle.

Classifying quadrilaterals

Secondary 1

TGM Original — E Math Summary Notes (4052), 2026 editorial manuscript

A diagonal divides a convex quadrilateral into two triangles, so its interior angles total $360^\circ$. Classify a quadrilateral from given properties; a tilted square remains a square.

Figure	Defining and useful properties
Parallelogram	Both pairs of opposite sides parallel; opposite sides and angles equal; diagonals bisect each other.
Rectangle	A parallelogram with four right angles; diagonals are equal.
Rhombus	A parallelogram with four equal sides; diagonals are perpendicular and bisect its angles.
Square	Both a rectangle and a rhombus; it has all their properties.
Trapezium	One pair of opposite sides parallel. An isosceles trapezium also has equal non-parallel sides and equal base angles.
Kite	Two pairs of adjacent equal sides; its symmetry diagonal bisects the other diagonal at right angles. The opposite angles between unequal sides are equal.

Example

In parallelogram $ABCD$, $\angle A=72^\circ$. Then $\angle C=72^\circ$, and $\angle B=\angle D=108^\circ$. If its diagonals meet at $M$ and $AC=14\text{ cm}$, then $AM=7\text{ cm}$.

A general kite does not have two diagonals that bisect each other. Equal diagonals alone do not prove that a quadrilateral is a rectangle.

Create a free account to practise similar questions.

Create free account Sign in Get the E Math course · from S$29.98/mo E Math tuition

Need help? Join our E-Maths tuition for O-Level success.

Learn more