4.3

Parallel lines

Cambridge IGCSE Mathematics (0580)  · Unit 4: Geometry  · 10 flashcards

Parallel lines is topic 4.3 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Triangles.  In one line: Parallel lines are lines in the same plane that never intersect, no matter how far they are extended. They have the same slope and are denoted by the symbol '||'.

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 10 flashcards — 2 definitions, 3 key concepts and 1 application card — covering the precise wording mark schemes reward.  Use the 2 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

Parallel lines

Parallel lines are lines in the same plane that never intersect, no matter how far they are extended. They have the same slope and are denoted by the symbol '||'.

Questions this Parallel lines deck will help you answer

Definition Flip

Define parallel lines.

Answer Flip

Parallel lines are lines in the same plane that never intersect, no matter how far they are extended. They have the same slope and are denoted by the symbol '||'.

Definition Flip

What is a transversal?

Answer Flip

A transversal is a line that intersects two or more parallel lines at distinct points. It creates various angle relationships, such as corresponding, alternate, and co-interior angles.

Key Concept Flip

Explain the relationship between corresponding angles formed by a transversal intersecting parallel lines.

Answer Flip

Corresponding angles are angles that occupy the same relative position at each intersection where the transversal crosses the parallel lines. Corresponding angles are congruent (equal).

Key Concept Flip

Describe the relationship between alternate interior angles formed by a transversal intersecting parallel lines.

Answer Flip

Alternate interior angles are angles that lie on opposite sides of the transversal and between the parallel lines. Alternate interior angles are congruent (equal).

Key Concept Flip

Explain the relationship between co-interior angles formed by a transversal intersecting parallel lines.

Answer Flip

Co-interior angles (also known as allied angles) are angles that lie on the same side of the transversal and between the parallel lines. Co-interior angles are supplementary, meaning they add up to 180 degrees.

Key Concept Flip

If one of the corresponding angles formed by a transversal intersecting two parallel lines is 65°, what is the measure of the other corresponding angle?

Answer Flip

Since corresponding angles are congruent, the other corresponding angle is also 65°.

Key Concept Flip

If one of the alternate interior angles formed by a transversal intersecting two parallel lines is 110°, what is the measure of the other alternate interior angle?

Answer Flip

Since alternate interior angles are congruent, the other alternate interior angle is also 110°.

Key Concept Flip

If one of the co-interior angles formed by a transversal intersecting two parallel lines is 70°, what is the measure of the other co-interior angle?

Answer Flip

Since co-interior angles are supplementary, they add up to 180°. Therefore, the other co-interior angle is 180° - 70° = 110°.

Key Concept Flip

Lines A and B are cut by a transversal. One angle formed is 50 degrees. If the co-interior angle on the same side of the transversal is 130 degrees, are lines A and B parallel? Explain.

Answer Flip

Yes, lines A and B are parallel. Co-interior angles are supplementary (add up to 180 degrees) if the lines are parallel. Since 50 + 130 = 180, the lines are parallel.

Key Concept Flip

In a diagram with parallel lines cut by a transversal, one angle is labeled 'x' and its corresponding angle is labeled '2x - 30'. Find the value of 'x'.

Answer Flip

Since corresponding angles are equal, x = 2x - 30. Solving for x gives x = 30 degrees.

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4.2 Angles in polygons 4.4 Triangles

Key Questions: Parallel lines

Define parallel lines.

Parallel lines are lines in the same plane that never intersect, no matter how far they are extended. They have the same slope and are denoted by the symbol '||'.

What is a transversal?

A transversal is a line that intersects two or more parallel lines at distinct points. It creates various angle relationships, such as corresponding, alternate, and co-interior angles.

More topics in Unit 4 — Geometry

Parallel lines 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.

parallel transversal corresponding angles alternate angles co-interior angles allied angles F-angles Z-angles

Key terms covered in this Parallel lines 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.

Parallel lines
Transversal

Related Mathematics guides

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How to study this Parallel lines deck

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