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Parallel and Intersecting Lines – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 5. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Two lines in a plane either intersect at a point or are parallel. A transversal cutting parallel lines creates equal and supplementary angle pairs.

Angles at intersecting lines

Vertically opposite angles are equal.
Angles on a straight line (linear pair) add to 180°.
Perpendicular lines meet at 90°.

Parallel lines and a transversal

Corresponding angles are equal.
Alternate interior angles are equal.
Interior angles on the same side add to 180°.
If any of these is true, the lines are parallel.

Key terms

Transversal: a line cutting two or more lines at different points
Parallel lines: lines in a plane that never meet
Linear pair: two adjacent angles forming a straight line

Formulas

Linear pair: a + b = 180°
Co-interior angles: a + b = 180°

Important questions with answers

Two lines intersect and one angle is 40°. Find the other three angles.2 marks

The vertically opposite angle is 40°; the other two are 180° − 40° = 140° each.

What are alternate interior angles? What is true about them when the lines are parallel?3 marks

They lie between the two lines on opposite sides of the transversal (forming a "Z" shape). When the lines are parallel, alternate interior angles are equal.

Two parallel lines are cut by a transversal. One angle is 65°. Find all the other seven angles and name the angle pairs you used.5 marks

Vertically opposite to 65° is 65°; linear pair gives 180° − 65° = 115°, and its vertically opposite angle is also 115°. At the other line, corresponding angles are equal, so again two angles are 65° and two are 115°. Pairs used: vertically opposite, linear pair, corresponding (alternate interior angles are also equal and co-interior angles add to 180°).

Quick revision

Vertically opposite angles are equal.
Corresponding and alternate angles are equal for parallel lines.
Co-interior angles add to 180°.

Exam tips

Mark equal angles with the same symbol in your figure.
Railway tracks and ruled notebook lines are everyday parallel lines.

Practice MCQs

Vertically opposite angles are
1. supplementary
2. always 90°
3. always equal
4. never equal
Show answer
Answer: (c) always equal. Equal.
Lines that never meet are
1. intersecting
2. parallel
3. perpendicular
4. curved
Show answer
Answer: (b) parallel. Parallel.
One angle of a linear pair is 115°. The other is
1. 65°
2. 75°
3. 115°
4. 245°
Show answer
Answer: (a) 65°. 180 − 115.
With parallel lines and a transversal, one corresponding angle is 70°. The other is
1. 110°
2. 70°
3. 20°
4. 90°
Show answer
Answer: (b) 70°. Corresponding angles are equal.
If two parallel lines are cut by a transversal and one corresponding angle is 70°, the other is
1. 110°
2. 20°
3. 70°
4. 140°
Show answer
Answer: (c) 70°. Corresponding angles are equal.
Two co-interior angles are (2x + 10)° and (3x − 30)°. Then x is
1. 30
2. 40
3. 50
4. 20
Show answer
Answer: (b) 40. 5x − 20 = 180.
If two lines are cut by a transversal and alternate angles are equal, the lines are
1. perpendicular
2. parallel
3. intersecting at 45°
4. the same line
Show answer
Answer: (b) parallel. Converse of alternate angle property.
Co-interior angles on the same side of a transversal between parallel lines are 3x and 2x. x is
1. 18°
2. 36°
3. 30°
4. 72°
Show answer
Answer: (b) 36°. 5x = 180°.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.