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Which shapes are divided into two mirror halves by the dotted line?

**Solution:**

Shapes that are divided into two mirror halves by the dotted line are:

Look at the figure in the white box. One 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.

**Solution:**

We will keep the mirror on a vertical dotted line to get shape (b).

Right part of the image will be hidden if we keep the mirror on a vertical dotted line.

Now make a line one the white box to show where you will keep the mirror to get the picture next to it.

**Solution:**

Venky has made a red and white shape. Make a line on the white 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.

**Solution:**

(b)

(c)

(d)

(e)

(1) Find out which letters in the English alphabet look the same after half a turn.

(2) Which of these English words reads the same on half a turn?

ZOOM, MOW, SWIMS, SIS, NOON

(3) Give half a turn to the numbers from 0 to 9.

Find which of them still looks the same.

(4) Think of all 2, 3 and 4 digit numbers which look the same on half a turn.

Example

2 digit numbers 1 1, _______, _______

3 digit numbers 1 0 1, 1 1 1, _______, _______, _______, _______, _______, ________

4 digit numbers 1 00 1, 1 1 1 1, _______, ________, ________, ________, ________

**Solution:**

(1) H, I, X, N, S, Z and O.

(2) MOW, SWIMS, SIS, and NOON read the same on half a turn.

(3) 0, 1 and 8 are the numbers that look the same after half a turn.

(4) 2 digit numbers that look the same on half a turn are __11__, __88__.

3 digit numbers that look the same on half a turn are __101__, __111__, __808__, __888__, __818__, __181__,

4 digit numbers that look the same on half a turn are __1001__, __1111__, __8008__, __8888__, __8118__, __1881__.

• Among the following shapes, find out which ones would look the same after $\frac{1}{4}$ turn. Put a (✓).

• Put a (✕) on the shapes that will not look the same after half a turn.

**Solution:**

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

**Solution:**

Draw what the following shapes would look like on $\frac{1}{4}$ turn and half a turn.

Which of the above shapes do not look the same on $\frac{1}{4}$ turn? Which shapes do not look the same on $\frac{1}{2}$ a turn?

**Solution:**

Image (a), (c) and (d) do not look the same on $\frac{1}{4}$ turn.

Image (a) does not look the same on $\frac{1}{2}$ turn.

Which fan will look the same on a $\frac{1}{3}$ turn?

**Solution:**

Fan (a) will look the same on $\frac{1}{3}$ turn.

• Can you see that this shape looks the same on $\frac{1}{6}$ turn?

• Look at the following shapes. Draw how they will look on $\frac{1}{3}\mathrm{and}\frac{1}{6}$ turn.

**Solution:**

Look at the following shapes ―

(a) Find out which of these figures look the same on $\frac{1}{3}$ turn. Mark them with (✓).

(b) Which are the ones that will not look the same after $\frac{1}{3}$ turn? Mark them with (✕).

(c) Try and change the shapes below in such a way that they look the same on $\frac{1}{3}$ turn.

**Solution:**

(a) and (b)

(c)

• Draw some shapes which will look the same after $\frac{1}{3}$ turn.

• Draw some shapes which will look the same after $\frac{1}{6}$ turn.

**Solution:**

- Figures that look the same after $\frac{1}{3}$ turn:

- Figures that look the same after $\frac{1}{6}$ turn:

**Disclaimer: **The answers may vary from student to student, based on his/her experience. The answers provided here are for reference only.