Parallel and Intersecting Lines
When lines meet or run side by side, they create angles with neat relationships. This Class 7 Ganita Prakash chapter studies intersecting and parallel lines, the angle pairs they form — complementary, supplementary, linear pair and vertically opposite — and the angles a transversal makes with parallel lines.
Learning objectives
- Distinguish intersecting and parallel lines.
- Identify complementary and supplementary angles.
- Use linear pair and vertically opposite angles.
- Recognise angles made by a transversal.
Key concepts
Intersecting and parallel lines
Two lines that cross at a point are intersecting lines, and the crossing point is common to both. Two lines in the same plane that never meet, staying the same distance apart, are parallel lines. The rails of a track are parallel; scissor blades are intersecting.
Complementary and supplementary angles
Two angles that add up to 90° are complementary, and two angles that add up to 180° are supplementary. So the complement of 30° is 60°, and the supplement of 110° is 70°. These pairs appear constantly in geometry problems.
Linear pair and vertically opposite angles
When two lines intersect, adjacent angles on a straight line form a linear pair and add to 180°. The angles directly across from each other are vertically opposite angles, and they are always equal. So at a crossing, opposite angles match and neighbouring angles are supplementary.
Transversal and parallel lines
A transversal is a line that cuts two other lines. When it crosses a pair of parallel lines, special equal angles appear: corresponding angles are equal and alternate angles are equal, while co-interior angles are supplementary. These facts let us find unknown angles.
Important formulas
Complementary angles
sum = 90°
Supplementary angles
sum = 180°
Linear pair
two adjacent angles on a line add to 180°
Key definitions
- Parallel lines
- Lines in a plane that never meet and stay the same distance apart.
- Linear pair
- Two adjacent angles on a straight line, adding to 180°.
- Vertically opposite angles
- The equal angles directly across an intersection.
- Transversal
- A line that crosses two or more other lines.
Solved examples
Q1. What is the complement of 35°?
Solution: 90° − 35° = 55°.
Q2. Two lines intersect; one angle is 70°. What is its vertically opposite angle?
Solution: 70°, since vertically opposite angles are equal.
Q3. What is the supplement of 110°?
Solution: 180° − 110° = 70°.
Common mistakes to avoid
- Mixing up complementary (90°) with supplementary (180°).
- Thinking vertically opposite angles add to 180° (they are equal).
- Assuming any two lines that look close are parallel.
- Confusing corresponding with alternate angles at a transversal.
Parallel and Intersecting Lines — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
Two angles that add up to 90° are:
Practice questions
Short answer
What are supplementary angles?
Two angles that add up to 180°.
Are vertically opposite angles equal or supplementary?
Equal.
What is a transversal?
A line that crosses two or more other lines.
Long answer
Explain linear pairs and vertically opposite angles formed when two lines intersect.
When two straight lines cross, four angles are formed at the point of intersection. Any two adjacent angles lie together on a straight line and form a linear pair, so they add up to 180°. The two angles that are directly across from each other — not adjacent — are called vertically opposite angles, and they are always equal to each other. So at a crossing, if one angle is 70°, the angle opposite it is also 70°, while each neighbouring angle is 180° − 70° = 110°. These relationships let us find every angle at the intersection once one is known.
Describe the angles formed when a transversal crosses two parallel lines.
A transversal is a line that cuts across two other lines. When the two lines are parallel, the transversal creates pairs of angles with fixed relationships. Corresponding angles (in matching positions at each crossing) are equal, and alternate angles (on opposite sides of the transversal, between the lines) are also equal. Co-interior angles, which lie on the same side between the parallel lines, are supplementary, adding to 180°. Using these rules, if one angle is known, all eight angles formed can be worked out — which is the basis for many geometry problems.
HOTS (Higher Order Thinking)
An angle is equal to its own complement. What is the angle?
45°, because 45° + 45° = 90°.
Two intersecting lines make one angle of 90°. What can you say about all four angles?
All four angles are 90° (right angles), since the lines are perpendicular.
Quick revision
Revision notes
- Intersecting lines cross; parallel lines never meet.
- Complementary add to 90°; supplementary add to 180°.
- Linear pair adds to 180°; vertically opposite angles are equal.
- Across parallel lines: corresponding and alternate angles equal.
Key takeaways
- Angle pairs have fixed sums or equalities.
- Vertically opposite angles are equal.
- Parallel lines and a transversal give equal angles.
Frequently asked questions
What is the difference between complementary and supplementary angles?
Complementary angles add to 90°; supplementary angles add to 180°.
Are vertically opposite angles equal?
Yes, they are always equal.
What is a linear pair?
Two adjacent angles on a straight line, adding to 180°.