12.2 Chapter summary
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12.1 Proofs and conjectures
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12.2 Chapter summary (EMA7J)
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A quadrilateral is a closed shape consisting of four straight line segments.
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A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
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Both pairs of opposite sides are equal in length.
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Both pairs of opposite angles are equal.
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Both diagonals bisect each other.
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A rectangle is a parallelogram that has all four angles equal to \({90}^{°}\)
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Both pairs of opposite sides are parallel.
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Both pairs of opposite sides are equal in length.
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The diagonals bisect each other.
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The diagonals are equal in length.
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All interior angles are equal to \({90}^{°}\)
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A rhombus is a parallelogram that has all four sides equal in length.
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Both pairs of opposite sides are parallel.
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All sides are equal in length.
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Both pairs of opposite angles are equal.
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The diagonals bisect each other at \(90°\)
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The diagonals of a rhombus bisect both pairs of opposite angles.
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A square is a rhombus that has all four interior angles equal to \(90°\)
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Both pairs of opposite sides are parallel.
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The diagonals bisect each other at \(90°\)
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All interior angles are equal to \(90°\)
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The diagonals are equal in length.
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The diagonals bisect both pairs of interior opposite angles (i.e. all are \(45°\))
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A trapezium is a quadrilateral with one pair of opposite sides parallel.
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A kite is a quadrilateral with two pairs of adjacent sides equal.
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One pair of opposite angles are equal (the angles are between unequal sides).
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The diagonal between equal sides bisects the other diagonal.
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The diagonal between equal sides bisects the interior angles.
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The diagonals intersect at \(90°\)
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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.
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