Class 7 Maths, Chapter 5 (NCERT). 15 questions by concept, 12 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
Two lines cross. The four angles formed are e above the crossing, f to its right, g below it and h to its left. Which of these is a pair of vertically opposite angles?
(d) e and g
Vertically opposite angles face across the intersection point. The pair e and g is opposite; each other offered pair is adjacent.
Two distinct straight lines on a sheet of paper cross. How many intersection points can they have?
(c) one point
Two distinct points determine one straight line. If two lines shared two distinct points, they would be the same line. Distinct crossing lines therefore have exactly one common point.
Line l crosses line t. One of the angles is 105°. How many of the four angles are right angles?
(a) 0
The vertically opposite angle is also 105°. Each neighbouring angle forms a linear pair with the given angle, so it equals 180° − 105° = 75°. Neither angle size is 90°, so there are 0 right angles.
On a flat page, two straight lines look curved because of short slanting strokes across them. Their perpendicular separation is 4 cm everywhere. A third line on the wall never meets them. Which pair is definitely parallel from this information?
(a) The two lines on the page; the wall line cannot be classified from this information.
The two lines on the page have a constant perpendicular separation, so they are parallel despite the visual illusion. The wall line is not necessarily parallel or non-parallel to them: its physical supporting surface alone does not settle its direction or coplanarity.
Two straight segments on a page do not touch, with one above the other. The perpendicular gap from the lower line to the upper line is 8 cm at one place and 3 cm at another. What rules out parallelism?
(c) The changing perpendicular gap
The two gaps are measured at right angles from the same lower line. Their sizes differ by 5 cm. Parallel lines stay the same distance apart, so these lines are not parallel. Separate drawn segments can still meet when their lines are extended.
A rectangular sheet of paper is folded exactly in half from left to right, aligning opposite edges. The still-folded stack is halved again the same way, then opened fully. How does each new crease lie relative to the first?
(b) It is parallel to it.
After the still-folded stack is halved again and opened fully, each new crease is distinct from and parallel to the first. The aligned opposite edges keep the folding direction fixed. A new crease is not automatically perpendicular to an earlier one.
Folding a square page in half once gives 3 parallel lines: the two edges and the crease. While still folded, it is folded in half again in the same direction, then opened. How many new creases does the second fold add?
(a) 2
After one fold there are 3 parallel lines with 2 gaps between them. The second fold puts one new crease in the middle of each gap, so it adds 2 creases. That gives 3 + 2 = 5 lines, not the doubled count of 6, which would need 3 new creases.
Two parallel lines are cut by a transversal. One interior angle measures 55°. What is the alternate angle -- the one between the lines on the OTHER side of the transversal, at the other crossing?
(b) 55°
Alternate interior angles of parallel lines are equal. The missing angle is 55°. Its same-side interior neighbour would instead measure 125°.
Two parallel lines are cut by a transversal. One interior angle measures 140°. What is the alternate angle -- the one between the lines on the OTHER side of the transversal, at the other crossing?
(b) 140°
Parallelism gives equality of corresponding angles; vertically opposite angles then give the alternate-interior equality. Thus the missing angle is 140°, not its supplement 40°.
A transversal crosses lines m and n at distinct points, and neither crossing is a right-angle crossing. At most, how many DIFFERENT sizes can there be among the eight angles formed?
(b) 4
Each of the two crossings contributes at most two sizes, so the maximum is four. The maximum is possible with, for example, 40°/140° at one crossing and 60°/120° at the other. Five or eight distinct sizes are impossible.
A transversal crosses lines l and t at two different points, forming eight angles. Which angle pairs are always equal at each crossing?
(c) Vertically opposite angles
Vertically opposite angles are equal at each crossing. Each angle has an equal opposite angle, so the eight angles cannot all have different measures. This holds whether or not the two lines are parallel.
Lines l and t lie on one flat surface and are not parallel. A transversal cuts them at two different points. The angle it makes at the first crossing is 55°. Its corresponding angle at the second crossing is . What must be true of ?
(c) x is not 55°
Corresponding angles are equal only when the two lines are parallel. Lines l and t are not parallel, so is not 55°. Nothing here fixes the exact size of , so 125° is not forced either.
A transversal cuts lines m and n on one flat surface at two different points. Corresponding angles measure exactly 72° and 76°. How are the two lines related?
(d) Intersecting
The corresponding angles differ by 4°, so the lines are not parallel. Distinct lines on one flat surface that are not parallel intersect when extended.
Two parallel lines are cut by a transversal. An obtuse interior angle is 110°. What is the interior angle at the other intersection on the same side of the transversal?
(a) 70°
Interior angles on the same side of a transversal cutting parallel lines add to 180°. The missing angle is 180° − 110° = 70°.
Lines p and q are parallel and are cut by a transversal that is not perpendicular to them. How many different angle sizes are there among the eight angles?
(a) 2
At one crossing, angles in a linear pair add to 180°. They have different sizes because the transversal is not perpendicular to the parallel lines. Vertically opposite angles repeat these two sizes. Corresponding angles are equal, so the same two sizes occur at the other crossing. There are exactly 2 different angle sizes.
Wrong
Alternate angles are equal even when a transversal crosses two nonparallel lines.
Why it feels right. The zigzag shape seems to be the whole rule.
Right
A transversal makes equal alternate angles when the two lines are parallel.
Worked example
