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Does this quadrilateral have only one pair of equal opposite angles?

Quadrilaterals (Properties) (F)

Know GCSE quadrilaterals: spot rectangles, parallelograms, kites and trapezia; use side, angle and diagonal facts to justify answers and solve perimeter and angle problems.

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Fascinating Fact:

In a picture frame, a rectangle has opposite sides equal and parallel, all angles = 90 degrees, and diagonals equal, so both diagonals match in length.

In GCSE Maths, you compare and classify quadrilaterals using their properties. Opposite sides may be parallel or equal, angles add to 360°, and diagonals can be equal, perpendicular, or bisect each other. These facts help you find unknown angles and lengths and justify reasons in proof-style questions.

Key Terms

Parallelogram: A quadrilateral with both pairs of opposite sides parallel; opposite sides and angles are equal, and diagonals bisect each other.
Kite: A quadrilateral with two pairs of adjacent equal sides; one pair of opposite angles is equal, and diagonals meet at right angles.
Diagonal: A straight line joining opposite vertices of a polygon; in quadrilaterals, diagonals may be equal, perpendicular, or bisect each other.

Frequently Asked Questions (Click to see answers)

What are the properties of a rectangle?

A rectangle has opposite sides equal and parallel, all angles 90°, and equal diagonals that bisect each other. It has two lines of symmetry and rotational symmetry of order 2.

How can I show a quadrilateral is a parallelogram?

Show any one of these: both pairs of opposite sides are parallel; both pairs of opposite sides are equal; one pair is parallel and equal; or the diagonals bisect each other.

What is the difference between a rhombus and a square?

Both have four equal sides and perpendicular, bisecting diagonals. A square also has all angles 90° and equal diagonals, so every square is a special rhombus.