A quadrilateral is a four-sided figure. The word is derived from Latin, where 'quadri' means four and 'latus' means sides.
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Definition of a rectangle?
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A rectangle is a quadrilateral with all angles equal to 90° and opposite sides of equal length.
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Properties of a rectangle?
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1. All angles are 90°. 2. Opposite sides are equal and parallel. 3. Diagonals are equal and bisect each other.
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What is a square?
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A square is a quadrilateral where all sides are equal, and all angles are 90°. Every square is a rectangle.
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Key properties of a square?
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1. All sides are equal. 2. All angles are 90°. 3. Diagonals bisect each other at right angles.
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What defines a parallelogram?
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A parallelogram is a quadrilateral with opposite sides that are parallel and equal.
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Properties of a parallelogram?
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1. Opposite sides are equal. 2. Opposite angles are equal. 3. Adjacent angles add up to 180°.
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What is a rhombus?
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A rhombus is a quadrilateral where all sides are of equal length. It is also a type of parallelogram.
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Diagonal properties of a rhombus?
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The diagonals of a rhombus bisect each other perpendicularly and also bisect the angles of the rhombus.
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What is a kite?
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A kite is a quadrilateral where two pairs of adjacent sides are equal. The diagonals intersect at right angles.
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What is a trapezium?
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A trapezium is a quadrilateral with at least one pair of parallel sides.
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Isosceles trapezium properties?
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An isosceles trapezium has one pair of parallel sides and the non-parallel sides are of equal length.
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Sum of angles in a quadrilateral?
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The sum of all interior angles in a quadrilateral is 360°.
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What are the diagonals of a rectangle?
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The diagonals of a rectangle are equal in length and bisect each other.
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What's unique about square's diagonals?
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The diagonals of a square are equal, bisect each other, and intersect at right angles.
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Congruence in quadrilaterals?
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Triangles can be used to establish congruence in quadrilaterals by using properties such as equal angles and sides.
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Definition of a trapezium?
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A trapezium is defined as a quadrilateral with at least one pair of parallel sides.
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What is a quadrilateral with equal sides?
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Quadrilaterals with equal sides can be rhombuses, squares, etc., but not all equal-sided quadrilaterals are squares.
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What is a Carpenter’s Problem?
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It illustrates how to construct rectangles using known lengths and properties of diagonals.
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Common mistakes in identifying quadrilaterals?
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Many confuse squares and rectangles due to similarities but they differ in side lengths; all squares are rectangles, but not all rectangles are squares.
