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NCERT Solutions for Class 7th Maths Chapter 1 In-text Questions — Geometric Twins

Book page 1–3 Updated on2026-09-19

Q1.
The symbol on this signboard needs to be recreated on another board. How do we do it?
Answer

One way is to trace the outline of the symbol on tracing paper and copy that outline on to the new board.

This works for a small symbol. For a big signboard it is not practical — you would need a huge sheet of tracing paper and a way to hold it flat against the board.

Why it happens: tracing copies every point of the figure, so nothing can go wrong. But it needs the original and the copy to be placed one over the other. When that is impossible, we must carry the information as numbers instead — a few measurements written down on paper.
Tip: A photograph will not do. A photo can be enlarged or reduced, so it fixes the shape but not the size.
Q2.
Can we take some measurements that would allow us to exactly recreate this figure? If yes, what measurements should we take?
The symbol on the signboard, page 1 — two straight arms meeting at a point.
Answer

Yes. Name the corner points of the symbol A, B and C as the book does. The symbol is just two straight arms joined at B.

Take these three measurements:

  • the length of the arm AB,
  • the length of the arm BC,
  • the angle ∠ABC between the two arms.
Why it happens: once BC is drawn, the arm BA can only be swung about B like the hand of a clock. The angle ∠ABC tells you exactly where to stop swinging, and the length AB tells you where to stop drawing. Nothing is left free, so the copy must be identical.
Q3.
Are the arm lengths AB and BC sufficient to exactly recreate this figure?
ABC
The same symbol with its corner points named A, B and C (page 1).
Answer

No. Two arm lengths are not enough.

Take AB = 4 cm and BC = 8 cm. Keeping both lengths fixed, the arms can still be opened out wide or closed up narrow. Every opening gives a different symbol.

A B C A B C A B C Same arms AB = 4 cm and BC = 8 cm, three different angles at B
The arm lengths are the same in all three, but the figures are clearly not copies of each other.
Why it happens: the two lengths pin down how far A and C are from B, but they say nothing about how far A is from C. The joint at B is still free to turn, like the hinge of a pair of scissors.
Q4.
To get the exact replica, would it help to take any other measurement?
Answer

Yes — measure the angle ∠ABC between the two arms.

AB = 4 cm
BC = 8 cm
∠ABC = 80°
→ only one symbol is possible
Why it happens: the angle locks the hinge at B. Once the opening is fixed, the position of A and the position of C are both decided, so the whole figure is decided. Three measurements — two arms and the angle between them — are enough to make an exact replica.
Q5.
Can you draw the symbol if it is known that AB = 4 cm, BC = 8 cm, and ∠ABC = 80°?
Answer

Yes. Here is the construction.

  1. Draw BC = 8 cm with a ruler.
  2. Place the protractor at B and mark 80° from BC. Draw a ray BX along that mark.
  3. From B, cut off BA = 4 cm on the ray BX.
  4. The bent line A–B–C is the required symbol.
80° A B C 8 cm 4 cm
Draw the longer arm first, then set the angle at B, then cut the shorter arm.
Check it yourself: ask a friend to draw the same three measurements on another sheet. Cut out both and place one over the other — they will fit exactly. The two symbols are congruent.
Q6.
If it is known that both symbols have the same arm lengths, can it be concluded that the two symbols are congruent?
Answer

No. Equal arm lengths are not enough.

We have already seen several symbols with AB = 4 cm and BC = 8 cm that are not copies of each other. They differ in the angle at B.

Same arms + different angle → not congruent
Same arms + same angle → congruent
Why it happens: fixing the angle fixes the shape and the size together. So to be sure that two such symbols are congruent, check three things — arm AB, arm BC, and the angle ∠ABC.
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