4.3

Parallel lines

10 flashcards to master Parallel lines

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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.

About Parallel lines (4.3)

These 10 flashcards cover everything you need to know about Parallel lines for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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