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Chapter Summary

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12.2 Chapter summary (EMA7J)

Presentation: 2GR2

  • 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