NCERT Solutions for Class 7th Maths Chapter 1 Figure it Out — Geometric Twins
Book page 3–4 Updated on2026-09-19
Q1.
Check if the two figures are congruent.
The two figures printed on page 3, drawn to the sizes given in the book.
Answer
They are not congruent.
Each figure is two arms joined at a point. Measure both arms and the angle in each figure:
Figure
Shorter arm
Longer arm
Angle between the arms
First
about 1.7 cm
about 3.4 cm
about 90°
Second
about 1.7 cm
about 3.4 cm
about 70°
The arms match, but the second figure is more closed at the corner.
Why it happens: the arm lengths agree, so the two figures pass the first test. But the angle at the corner is not the same, and the angle is exactly what fixes the shape. Trace the first figure and try to place it on the second — the arms will never lie along each other at the same time.
Tip: measure the angles in your own book with a protractor. Printing can shift a line slightly, so trust your own measurement.
Q2.
Circle the pairs that appear congruent.
Answer
Two of the four pairs are congruent.
Pair
Congruent?
Reason
The two teardrops
Yes
Same size and shape; the second one is only turned (rotated) so its tip points left
The two clouds
No
The first cloud is bigger and has more bumps along its edge
The two bursts (stars)
No
Same shape, but one is clearly smaller than the other
The two leaf pairs
Yes
The second is the mirror image (flip) of the first; each leaf matches its partner
Why it happens: while checking congruence a figure may be rotated or flipped before it is placed on the other. So the turned teardrop and the flipped leaf pair still count as congruent. Being a smaller copy, however, is never allowed — congruent figures must have the same size, not just the same shape.
Check it yourself: trace each left-hand figure on tracing paper. Slide, turn and even flip the paper over. If it settles exactly on its partner, the pair is congruent.
Q3.
What measurements would you take to create a figure congruent to a given: (a) Circle (b) Rectangle. Using this, state how would you check if two — (a) Circles are congruent? (b) Rectangles are congruent?
Answer
(a) Circle — one measurement is enough: the radius (or the diameter, which is twice the radius).
Radius r → open the compass to r → draw the circle Two circles are congruent ⟺ their radii are equal
(b) Rectangle — two measurements: the length and the breadth.
Length l and breadth b → draw l, turn 90°, draw b, and close up Two rectangles are congruent ⟺ same length and same breadth
Why it happens: a circle has nothing to fix except how far its boundary is from the centre, so one number decides everything. A rectangle already has all four angles equal to 90°, so only the two side lengths are left free. Nothing else needs to be measured.
Tip: for the rectangles, compare the longer side with the longer side and the shorter with the shorter. A 3 cm × 5 cm rectangle is congruent to a 5 cm × 3 cm one — the second is just standing on its side.
Q4.
How would we check if two figures like the one below are congruent? Use this to identify whether each of the following pairs are congruent.
Answer
The figure is made of two straight strokes that meet at a point. Three arms come out of that meeting point, so measure:
the three arm lengths from the meeting point, and
the angles between the arms.
If the arms and the angles match up in the same order, the figures are congruent — a figure may be turned or flipped first.
Measure every arm from the meeting point, and the angles between neighbouring arms.
The two pairs given in the book: measure them and you will find that in both pairs the arms and the angles agree exactly. So both pairs are congruent — in each pair one figure is simply the other shifted to a new place on the page.
Why it happens: sliding a figure to a new position changes nothing about it. Length and angle do not depend on where the figure sits on the paper, so a shifted copy is always congruent to the original.
Check it yourself: trace one figure of a pair and slide the tracing paper across — without turning it — on to its partner. It fits exactly.