NCERT Solutions Ganita Prakash Chapter 8 In-text Questions — Squares and Rectangles

Book page 193 Updated on2026-09-05

Q1.

So, can a rectangle be named using any combination of the labels around its corners? For example, it cannot be named ABDC or ACBD. Can you see what names are allowed and what names are not?

Answer

No, any combination is not allowed. A name is valid only if the letters follow the corners in the order in which you travel around the boundary, starting from any corner and going either clockwise or anticlockwise.

For the rectangle of Fig. 8.4 (A top-left, B top-right, C bottom-right, D bottom-left):

Allowed names (8 in all)	Not allowed
ABCD, BCDA, CDAB, DABC	ABDC
ADCB, DCBA, CBAD, BADC	ACBD, ACDB, BDAC …

Why: the name has to tell you which corners are joined. In ABCD the sides are AB, BC, CD and DA — all four are real sides. In ABDC the letters ask you to join B to D, which is a diagonal, not a side. So the name describes a different figure altogether.

Quick test: read the letters in a circle. If every neighbouring pair (including the last with the first) is a side of the figure, the name is valid.

Q2.

Which of the following is not a name for this square? 1. PQSR 2. SPQR 3. RSPQ 4. QRSP

Answer

In the given square, going round the boundary the corners come in the order S → P → Q → R → S (S top-left, P top-right, Q bottom-right, R bottom-left).

Name	Sides it asks for	Valid?
1. PQSR	PQ, QS, SR, RP	No — QS and RP are diagonals
2. SPQR	SP, PQ, QR, RS	Yes
3. RSPQ	RS, SP, PQ, QR	Yes
4. QRSP	QR, RS, SP, PQ	Yes

Answer: option 1 — PQSR is not a name for this square.

Why it happens: options 2, 3 and 4 are the same round trip started from different corners. PQSR jumps from Q straight to S, and Q and S are opposite corners — that is a diagonal, so the letters no longer travel around the boundary.

Q3.

Here is a square piece of paper having all its sides equal in length and all angles equal to 90°. It is rotated as shown in the figure. Is it still a square?

Answer

Yes, it is still a square. Check the two properties of a square on the rotated paper:

S1 — Are all the sides still equal? Yes. Turning the paper does not stretch or shrink any side.
S2 — Are all the angles still 90°? Yes. Turning the paper does not open or close any corner.

The same piece of paper, turned. Sides and angles are untouched, so both properties S1 and S2 still hold.

Why it happens: a shape is a square because of its lengths and angles, not because of the direction it faces. Rotation moves the figure but changes no measurement. By the same reasoning, a rotated rectangle is still a rectangle.

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