NCERT Solutions
Make Your Pattern

1.Can you cut this pattern in such a way that you get two similar mirror halves? In how many ways can you do it?
Ans. Yes, I can cut this pattern to get two similar mirror halves. It can be done in only one way.

NCERT Solutions
1.Which shapes are divided into two mirror halves by the dotted line?
Ans. Following shapes are divided into two mirror halves by dotted line:
1, 2, 4, 5, 6, 7, 8, 10 and 15

NCERT Solutions
Mirror Games
1.Look at the figure in the white box. On which of the dotted lines will you keep the mirror so that you get shape (b)? Also tell which part of the picture will be hidden when we keep the mirror on the dotted line.

Ans. The mirror needs to be kept on the vertical dotted line.
The part of the picture which is on the right side of the dotted line will be hidden when mirror is kept on the dotted line.

NCERT Solutions
1.Now make a line on the white box to show where you will keep the mirror to get the picture next to it.
Ans. Following pictures show the position of dotted lines to get the figure as shown in questions.

2.Venky has made a red and white shape. Make a line on the white box where box where you will keep a mirror to get that shape. Look at how the line is drawn in the first box to get the picture next to it.
Ans. Following pictures show the position of dotted lines to get the figure as shown in questions

NCERT Solutions
Half A Turn
1.Once there was a king. He was upset because thieves kept stealing costly jewels from his locker. Here is what the locker looked like:

The locker could be opened by giving its handle half a turn. Another half turn and the locker would be locked again.

The king would often leave the locker open thinking it was locked. Can you guess the reason?
Ans. The looks same in both positions. Hence, the king often gets confused and cannot tell if it is locked or open.

NCERT Solutions
1.One day his clever daughter gave him an idea which he liked very much. Now he never got confused.Can you guess what the idea was?

Ans. The king’s daughter put a dot on one of the yellow blades on the lock. This helped in knowing the position of lock by the position of the dot.

2.The king had many such lockers with different handles. Check if, on giving them half a turn, he can get confused with these too.

What will you do to solve the problem for each of these?
Ans. We can put dots on these locks to stop confusion.

Same After 1/2 Turn?
1.Guess which of the shapes below would look the same after half a turn.

Ans. All figures, except the last figure, would look the same after half a turn.
Do you find it difficult to tell? If yes, then there is a way to check your guess. Here’s how you can do it.
Take out any of the shape. Trace its outline on a sheet of paper. Now keep the shape on its outline and give it half a turn. See if the shape fits its outline.

NCERT Solutions
Practice Time
1.Find out which letters in the English alphabet look the same after half a turn.
Ans. Following letters in the English alphabet look the same after half a turn.
H, I, N, O, S, X and Z

2.Which of these English words reads the same on half a turn?
ZOOM, MOW, SWIMS, SIS, NOON
Ans. Following words read the same on half a turn:
MOW, SWIMS, SIS and NOON

3.Give half a turn to the numbers from 0 to 9. Find which of them still looks the same.
Ans. Following numbers look the same after half a turn:0, 1 and 8

4.Think of all 2, 3 and 4 digit numbers which look the same on half a turn.
Ans. Some examples are given below:
2.digit numbers: 11, 88
3.digit numbers: 101, 111, 181, 808, 888
4.digit numbers: 1001, 1111, 1881, 8008, 8118, 8888

5.Which among the following pictures will look the same on half a turn?

Ans. Following pictures will look the same on half a turn:(a), (c), (f) and (h)

NCERT Solutions
Activity Time
1.Have you ever seen a windmill? What is it used for?
Ans. Yes, I have seen a windmill.
The windmill is used for grinding corn, pumping water. It is also used for generating electricity.

2.Does your windmill look the same on 1/4 of the turn?
Ans. Yes, it looks the same on 1/4 of the turn.

3.Does it look the same on half a turn? Discuss.
Ans. Yes, it looks the same on half a turn. The half turn is equal to two 1/4 turns and hence the windmill looks the same.

NCERT Solutions
One-fourth Turn
1.Does the fan look the same on 1/4 turn?
Ans. Yes, the fan looks the same on 1/4 turn.

2.Will this fan also look the same after 1/4 turn? Draw in the yellow box.
Ans. No, this fan does not look the same after 1/4 turn. It can be shown as the picture on the right.

NCERT Solutions
Practice Time
1.

Ans.

(B)Try and change the shapes in such a way that the new shape remains the same on giving it half a turn.

Ans. Given shapes can be changed so that the new shape remains the same on giving it half a turn.

(C)Draw what the following shapes would look like on 1/4 turn and half a turn.

Ans.

2.Which fan will look the same on a 1/3 turn?

Ans. Fan (a) will look the same after 1/3 turn.

3.Draw this shape after 1/3 turn.

Ans.

NCERT Solutions
One-sixth Turn
1.Can you see that this shape looks the same on 1/6 turn?

Ans. Yes, the shape looks the same on 1/6 turn.

Practice Time
1.Look at the following shapes. Draw how they will look on 1/3 and 1/6 turn.
Ans. Given shapes are shown in the table after 1/3 and 1/6 turns.

2.

Ans.

(c)Try and change the shapes below in such a way that they look the same on 1/3 turn.
Ans.

3.Draw some shapes which will look the same after 1/3 turn,
Draw some shapes which will look the same after 1/6 turn.
Ans. For both 3 and 4; following figures will look the same after 1/3 and 1/6 turn.