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12.2 Chapter summary (EMA7J)

A quadrilateral is a closed shape consisting of four straight line segments.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Both pairs of opposite sides are equal in length.

Both pairs of opposite angles are equal.

Both diagonals bisect each other.


A rectangle is a parallelogram that has all four angles equal to \({90}^{°}\)

Both pairs of opposite sides are parallel.

Both pairs of opposite sides are equal in length.

The diagonals bisect each other.

The diagonals are equal in length.

All interior angles are equal to \({90}^{°}\)


A rhombus is a parallelogram that has all four sides equal in length.

Both pairs of opposite sides are parallel.

All sides are equal in length.

Both pairs of opposite angles are equal.

The diagonals bisect each other at \(90°\)

The diagonals of a rhombus bisect both pairs of opposite angles.


A square is a rhombus that has all four interior angles equal to \(90°\)

Both pairs of opposite sides are parallel.

The diagonals bisect each other at \(90°\)

All interior angles are equal to \(90°\)

The diagonals are equal in length.

The diagonals bisect both pairs of interior opposite angles (i.e. all are \(45°\))


A trapezium is a quadrilateral with one pair of opposite sides parallel.

A kite is a quadrilateral with two pairs of adjacent sides equal.

One pair of opposite angles are equal (the angles are between unequal sides).

The diagonal between equal sides bisects the other diagonal.

The diagonal between equal sides bisects the interior angles.

The diagonals intersect at \(90°\)


The midpoint theorem: The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side.
This video shows how to prove that the opposite sides of a parallelogram are equal.
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