Worksheet Solutions: Parallel and Intersecting Lines | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Section A: Identify the Type of lines

Q1. Classify the following pairs of lines as Parallel (P), Perpendicular (⊥), or Intersecting (I):
a) Opposite edges of a book
b) Hands of a clock at 9:00
c) Letter "T"
d) Railway tracks
e) Corners of a window frame

Ans:  a) Opposite edges of a book
These edges run side by side and remain the same distance apart; they never meet even if extended.
⇒ Parallel (P)

b) Hands of a clock at 9:00
At 9:00 the minute hand points to 12 and the hour hand points to 9. The two hands meet at a right angle (90°).
⇒ Perpendicular (⊥)

c) Letter "T"
The vertical line and the top horizontal line meet and form a right angle where they cross.
⇒ Perpendicular (⊥)

d) Railway tracks
Both rails stay the same distance apart along their length and do not meet; they run side by side.
⇒ Parallel (P)

e) Corners of a window frame
The vertical and horizontal edges meet at each corner and form right angles.
⇒ Perpendicular (⊥)

Section B: Numerical Based Questions

Q2. Two lines intersect to form four angles. If one angle is 70°, find the measures of the other three angles.

Ans: One angle is 70°.
Vertically opposite angle is equal to it, so one more angle is 70°.
The angles adjacent to a 70° angle form a linear pair with it, so each adjacent angle = 180° - 70° = 110°.
Therefore, the other three angles are: 70°, 110°, and 110°.

Q3. In the figure below, line l ∥ m and transversal t cuts them. If ∠2 = 65°, find ∠6.

Ans: Because l ∥ m, corresponding angles made by the transversal t are equal.
Angle ∠6 corresponds to ∠2, so ∠6 = 65°.

Section C: Theory Based Questions

Q4. Define:
a) Parallel lines
b) Perpendicular lines

Ans:
a) Parallel lines are lines in the same plane that never meet no matter how far they are extended; they stay the same distance apart.
b) Perpendicular lines are two lines that intersect and form a right angle of 90° at their point of intersection.

Q5. Identify the type of angles formed when two lines intersect:
a) Angles opposite each other
b) Adjacent angles forming a straight line

Ans:
a) Angles opposite each other are called vertically opposite angles. They are equal in measure.
b) Adjacent angles that form a straight line are called a linear pair. Their measures add to 180°.

Q6. Two railway tracks are said to be parallel. A boy standing on a bridge drops a straight stick that cuts across both tracks.
What is the name of the stick in geometric terms?
Also, name any two pairs of angles formed and say if they are equal.

Ans: The stick acts as a transversal because it cuts across the two parallel tracks.
Two pairs of angles formed and their equality:

• Corresponding angles → These lie in the same relative position at each intersection of the transversal with the parallel tracks; they are equal.
• Alternate interior angles → These lie on opposite sides of the transversal and between the two parallel lines; they are equal.