A figure has point symmetry, if it has a rotational symmetry of 180 degrees.

How to check if a shape has symmetry about a point :

**One way to check if a figure has symmetry about a point would be to turn it upside down. If the figure looks the same as the original then it has symmetry about a point.**

**However, we can use the following two conditions to check whether a shape has symmetry about a point. **

**(i) Every part of the given shape must have a matching part must be at the same distance from the central point**

**(ii) The part of the shape and its matching part must be in the opposite direction. **

**Note : **

Symmetry about a point is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is symmetrical.

**Example :**

**Problem 1 :**

State if playing card given below has symmetry about a point.

**Solution : **

**Yes**

**In the playing card given above, we have **

**(i) Every part of the card has a matching part are at the same distance from the central point.**

**(ii) The part of the playing card and its matching part are in the opposite direction. **

**More clearly, **

**Problem 2 :**

State if the shape given below has symmetry about a point.

**Solution : **

**Yes**

**In the shape given above, we have**

**(i) Every part of the shape has a matching part are at the same distance from the central point.**

**(ii) The part of the shape and its matching part are in the opposite direction. **

**More clearly, **

**Problem 3 :**

State if the shape given below has symmetry about a point.

**Solution : **

**No **

**The shape given above does not satisfy the second condition of point of symmetry. **

**That is, **

**The part of the shape and its matching part are not in the opposite direction. They are in the same direction.**

**More clearly, **

**Problem 4 :**

State if the shape given below has symmetry about a point.

**Solution : **

**Yes**

**In the shape given above, we have**

**(i) Every part of the shape has a matching part are at the same distance from the central point.**

**(ii) The part of the shape and its matching part are in the opposite direction. **

**More clearly, **

**Problem 5 :**

State if the shape given below has symmetry about a point.

**Solution : **

**No **

**The shape given above does not satisfy the first condition of point of symmetry. **

**That is, **

**The part of the shape and its matching part are not at ****the same distance from the central point.**

**More clearly, **

**Problem 6 :**

State if the shape given below has symmetry about a point.

**Solution : **

**Yes**

**In the shape given above, we have**

**(i) Every part of the shape has a matching part are at the same distance from the central point.**

**(ii) The part of the shape and its matching part are in the opposite direction. **

**More clearly, **

**Problem 7 :**

State if the shape given below has symmetry about a point.

**Solution : **

**Yes**

**In the shape given above, we have**

**(i) Every part of the shape has a matching part are at the same distance from the central point.**

**(ii) The part of the shape and its matching part are in the opposite direction. **

**More clearly, **

**Problem 8 :**

State some English alphabets which exhibit symmetry about a point.

**Solution : **

The English alphabets Z, H, N and O exhibit point symmetry.

More clearly,

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