4.5

Quadrilaterals

Cambridge IGCSE Mathematics (0580)  · Unit 4: Geometry  · 9 flashcards

Quadrilaterals is topic 4.5 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines.  In one line: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. This parallelism is the defining characteristic.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 3 definitions and 6 key concepts — covering the precise wording mark schemes reward.  Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

The defining property that distinguishes a parallelogram from other quadrilaterals

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. This parallelism is the defining characteristic.

Questions this Quadrilaterals deck will help you answer

Definition Flip

What is the defining property that distinguishes a parallelogram from other quadrilaterals?

Answer Flip

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. This parallelism is the defining characteristic.

Definition Flip

A quadrilateral has two pairs of equal length sides that are adjacent to each other. Name the quadrilateral.

Answer Flip

The quadrilateral is a kite. Kites have two pairs of adjacent sides that are equal in length and diagonals that intersect at right angles.

Key Concept Flip

A square has rotational symmetry of order ___ and ___ lines of symmetry.

Answer Flip

A square has rotational symmetry of order 4 (90°, 180°, 270°, 360°) and 4 lines of symmetry (through opposite sides and corners).

Key Concept Flip

State one property that a rhombus possesses that a parallelogram does not necessarily have.

Answer Flip

A rhombus has all four sides of equal length. A parallelogram only requires opposite sides to be of equal length.

Definition Flip

A quadrilateral has exactly one pair of parallel sides. What is the name of this quadrilateral?

Answer Flip

This quadrilateral is a trapezium (or trapezoid). Only one pair of sides needs to be parallel for it to be classified as a trapezium.

Key Concept Flip

The diagonals of a quadrilateral bisect each other at right angles. Identify two possible quadrilaterals it could be.

Answer Flip

The quadrilateral could be a rhombus or a square. Both of these quadrilaterals have diagonals that bisect each other at right angles.

Key Concept Flip

What is the sum of the interior angles of any quadrilateral?

Answer Flip

The sum of the interior angles of any quadrilateral is 360 degrees. This holds true regardless of the specific type of quadrilateral.

Key Concept Flip

A rectangle has diagonals of length 10cm. What can you say about the length of each diagonal segment from the point of intersection of diagonals to each corner.

Answer Flip

The diagonals of a rectangle are equal in length and bisect each other. Therefore, each diagonal segment is 5cm long.

Key Concept Flip

Is it possible for a square to also be a rhombus? Explain.

Answer Flip

Yes, a square is a special type of rhombus. A rhombus must have four equal sides, which a square also possesses. A square simply adds the requirement of four right angles.

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4.4 Triangles 4.6 Circles

Key Questions: Quadrilaterals

What is the defining property that distinguishes a parallelogram from other quadrilaterals?

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. This parallelism is the defining characteristic.

A quadrilateral has two pairs of equal length sides that are adjacent to each other. Name the quadrilateral.

The quadrilateral is a kite. Kites have two pairs of adjacent sides that are equal in length and diagonals that intersect at right angles.

A quadrilateral has exactly one pair of parallel sides. What is the name of this quadrilateral?

This quadrilateral is a trapezium (or trapezoid). Only one pair of sides needs to be parallel for it to be classified as a trapezium.

Tips to avoid common mistakes in Quadrilaterals

More topics in Unit 4 — Geometry

Quadrilaterals sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

quadrilateral square rectangle parallelogram rhombus trapezium kite properties diagonal symmetry

Key terms covered in this Quadrilaterals deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

The defining property that distinguishes a parallelogram from other quadrilaterals
A quadrilateral has two pairs of equal length sides that are adjacent to each other. Name the quadrilateral
A quadrilateral has exactly one pair of parallel sides. What is the name of this quadrilateral

Related Mathematics guides

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How to study this Quadrilaterals deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.