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Primary 6 Special quadrilaterals

A quadrilateral is a closed, flat shape with four straight sides and four corners. Its four interior angles add up to 360°. Squares, rectangles, parallelograms, rhombuses, and trapeziums are all quadrilaterals.

Square

  • All four sides are equal.
  • All four angles are right angles: 90°.
  • Opposite sides are parallel.
  • A diagonal joins opposite corners and divides each corner angle into two equal angles.
xequal sides
The diagonal bisects the 90° angle at the top-left corner.

Find the angle made by the diagonal

A diagonal splits one corner of a square into two equal angles. Find x.

Rectangle

  • Opposite sides are equal and parallel.
  • All four angles are right angles: 90°.
  • A diagonal can split a corner into two angles that add to 90°. They are not necessarily equal.
32°x
The two marked angles together make a right angle.

Find the other part of a corner

A diagonal splits a rectangle corner. One angle is 32°. Find x.

Triangle

A triangle has three sides, so it is not a quadrilateral. Its angle facts help when a quadrilateral is divided into triangles.

  • The three interior angles add to 180°.
  • In an isosceles triangle, two sides are equal.
  • The angles opposite those equal sides are equal.
40°xx
The green marks show equal sides, so the base angles are equal.

Find a base angle

An isosceles triangle has a top angle of 40°. Find each base angle, x.

Parallelogram

  • Both pairs of opposite sides are parallel and equal.
  • Opposite angles are equal.
  • Adjacent angles add to 180°.
70°x
Matching arrows show both pairs of parallel sides.

Find an adjacent angle

One angle in a parallelogram is 70°. Find the angle x beside it.

Rhombus

  • All four sides are equal.
  • Opposite sides are parallel, and opposite angles are equal.
  • Adjacent angles add to 180°.
  • A diagonal bisects the angles at the two corners it joins.
80°x
Side ticks show equal lengths; matching arrows show parallel sides. The diagonal halves the top angle.

Find half of a rhombus angle

The top angle of a rhombus is 80°. A diagonal splits it in half. Find x.

Trapezium

  • The marked pair of opposite sides is parallel.
  • Angles inside the shape on the same side of a sloping edge add to 180°.
  • The four interior angles still add to 360°.
x115°
Angles along the left side lie between two parallel lines.

Find an angle beside a sloping side

The top and bottom of a trapezium are parallel. The bottom-left angle is 115°. Find x at the top-left.

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