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# 12.2 Chapter summary

## 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 mid-point theorem: The line joining the mid-points 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.

Video: 2GR3

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