7.5 Chapter summary

7.5 Chapter summary (EMA67)

Presentation: 2G86

• 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 states that 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.