Quadrilaterals

Properties of parallelograms, rectangles, rhombuses, squares, trapeziums and kites, and the angle sum of a quadrilateral.

Special quadrilaterals

A diagonal splits any quadrilateral into two triangles, so the angles add to $2 \times 180^\circ = 360^\circ$.

Example 1●

A quadrilateral has angles $85^\circ$, $110^\circ$ and $72^\circ$. Find the fourth.

$360 - 85 - 110 - 72 = 93^\circ$

Example 2●●

In parallelogram $ABCD$, $\angle A = 65^\circ$. Find the other angles.

$\angle D = 180 - 65 = 115^\circ$

Co-interior angles, AB ∥ DC

$\angle C = 65^\circ$, $\angle B = 115^\circ$.

Opposite angles of a parallelogram are equal

Flashcards

Angle sum of a quadrilateral

$360^\circ$

Rhombus diagonals

Bisect each other at right angles.

Rectangle diagonals

Equal in length and bisect each other.

Practice

A quadrilateral has angles $85^\circ$, $110^\circ$, $72^\circ$. Find the fourth.
In parallelogram $ABCD$, $\angle A = 65^\circ$. Find $\angle B$.
Which quadrilateral has diagonals that are equal but not necessarily perpendicular?
A parallelogram with four equal sides is a:
At what angle do the diagonals of a kite meet?
A kite has angles $120^\circ$, $x^\circ$, $100^\circ$, $x^\circ$. Find $x$.
Is every rectangle a square?
A quadrilateral has angles $x^\circ$, $x^\circ$, $2x^\circ$ and $2x^\circ$. Find $x$.