NCERT Solutions Ganita Prakash (Part 1) Chapter 5 In-text Questions — Across the Line
Book page 107 Updated on2026-09-05
Q1.
Can two straight lines intersect at more than one point?
Answer
No. Two different straight lines can meet at only one point.
Why it happens: Through any two points there is exactly one straight line. So if two lines had two common points P and Q, both lines would have to be the same line through P and Q — they would not be two different lines at all.
Tip: Try it with two rulers on your desk. Once the edges cross at one point, they immediately start moving apart on both sides.
Q2.
Activity 1: Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection. What patterns do you observe among these angles?
Answer
Whatever pair you draw, the same two patterns show up every time.
A sample set of readings from four different drawings:
Drawing
∠a
∠b
∠c
∠d
∠a + ∠b
1
120°
60°
120°
60°
180°
2
90°
90°
90°
90°
180°
3
35°
145°
35°
145°
180°
4
72°
108°
72°
108°
180°
Tip: If your readings are a degree or two off, it is the protractor and the thickness of the pencil line — not the mathematics. Draw thin lines and read the protractor with your eye straight above the mark.
Q3.
In Fig. 5.2, if ∠a is 120°, can you figure out the measurements of ∠b, ∠c and ∠d, without drawing and measuring them?
Why it happens: ∠a and ∠b sit side by side on a straight line, so together they make a straight angle of 180°. The same is true of the next pair, and the next — that chain of 180°s is what forces the facing angles to be equal.
Q4.
Is this always true for any pair of intersecting lines? Check this for different measures of ∠a. Using these measurements, can you reason whether this property holds true for any measure of ∠a?
Answer
Yes, it is always true — and we can prove it without using any particular number.
∠a + ∠b = 180° (straight angle on one line) ∠a + ∠d = 180° (straight angle on the other line) So ∠a + ∠b = ∠a + ∠d Take ∠a away from both sides → ∠b = ∠d
Why it happens: Both ∠b and ∠d are "what is left over" from 180° after removing the same angle ∠a. Two numbers that fill the same gap must be equal. Notice that no measurement was used — this is a proof, and it works for every value of ∠a.
Did you know? Angles like ∠a and ∠b are called a linear pair, and angles like ∠b and ∠d are called vertically opposite angles. This little argument is one of the first proofs in your geometry course.