Class 7 Mathematics

Chapter 5 Solutions — Parallel and Intersecting Lines

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Step-by-step NCERT solutions for Parallel and Intersecting Lines (Chapter 5, NCERT Class 7 Mathematics) — the full working for every question, not just the final answer. You can also read the Parallel and Intersecting Lines textbook chapter.

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All 11 questions in Parallel and Intersecting Lines are solved in the PDF. Here's what's inside, exercise by exercise:

Across the Line — Intersecting Lines

In Fig. 5.3, lines l and m intersect at a point forming four angles labelled a, b, c, d (a is top-left, b is top-right, c is bottom-right, d is bottom-left). List all the linear pairs and all the pairs of vertically opposite angles.

Between Lines — Parallel Lines

In Fig. 5.6, several line segments are drawn on a dot paper: a (diagonal, top-left), b (diagonal, left-lower), c (diagonal, crossing through the grid), d (short diagonal, top-centre), e (diagonal, top-right area), f (diagonal, lower-right area), g (diagonal, centre-right), h (short, lower-centre), i (short, lower-centre). Which pairs of lines appear to be parallel?

Parallel and Perpendicular Lines in Paper Folding

1.
In Fig. 5.11, a grid-based figure is shown with various line segments forming shapes. Mark the parallel lines using arrow notation (single arrow, double arrow, etc.) and mark perpendicular lines with a square symbol.
- (a) How did you spot the perpendicular lines?
- (b) How did you spot the parallel lines?
In Fig. 5.13, three line segments a, b, and c are shown: a is at the bottom, c is just above and parallel-looking to a, and b is slightly above c. Which line is parallel to line a — line b or line c? How do you decide this?

Drawing Parallel Lines

In Fig. 5.23, a line l and a point A (above the line) are given. Can you draw a line parallel to l that goes through point A? Describe your method using the tools from your geometry box.

Alternate Angles and Parallel Line Properties

1.
Find the angles marked a through j in Fig. 5.30. Each sub-figure shows either two parallel lines (marked with arrows) cut by a transversal, or lines meeting at a point. The given angles are:
- (a) 48°;
- (b) 52° with parallel lines;
- (c) 99° and 81° with parallel lines;
- (d) 81° and 99° at lower intersection with parallel lines, d° at upper;
- (e) 97°, 83°, and 69° at a multi-line intersection;
- (f) 132°…
2.
Find the angle represented by a in each sub-figure of Fig. 5.31.
- (i) Three parallel lines (with arrows) cut by transversals; 42° is at the upper-right and 100°, a° are at the lower crossing.
- (ii) Two parallel lines cut by transversal; 62° is at upper crossing, a° is at the lower crossing on the opposite side.
- (iii) Three parallel horizontal lines cut by a bent transversal; 110° is at the top…
3.
In Fig. 5.32, what angles do x and y stand for?
- (i) Two parallel horizontal lines: a vertical transversal meets the upper parallel at a right angle (90°); a diagonal line meets the lower parallel at 65° on the right; x° is the angle between the diagonal and the vertical transversal below the lower parallel; y° is the supplement of x.
- (ii) Two parallel horizontal lines: two transversals meet the…
In Fig. 5.33, two parallel horizontal lines are shown: the upper line passes through points I–K–B–A (left to right) and the lower line passes through G–E–D (left to right). One transversal runs J–K–E–F (J at top, then down through K on the upper line, through E on the lower line, ending at F below-right of E); the other transversal runs C–B–E–H (C at top-right, then down through B on the upper…
In Fig. 5.34, AB, CD, and EF are three parallel lines (vertical, with upward arrows). EA is a horizontal line perpendicular to all three. A diagonal line passes through B (on AB), D (on CD), and F (on EF), making ∠BEF = 55° at E (the angle between this diagonal and EF). x° is the angle the diagonal makes with AB at B; y° is the angle it makes with CD at D. Find x and y.
In Fig. 5.35, L is at the top and M is at the bottom-left; LM is a straight line. N is a point on a horizontal line LN (to the right of L). O is below-right of N. P is to the upper-right and Q is below P; PQ is a straight line. ∠LNO = 96° (angle at N between NL leftward and NO going down-right) and ∠OPQ = 52° (angle at P between OP going up-left and PQ going down). ∠NLM = 40° (angle at L between…

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