Symmetry Worksheet - Teach On - Free Printable

Problem Description:

The task is to identify which objects in the given images are symmetrical. Symmetry can be of two types:
1. Reflection symmetry (or mirror symmetry): An object has reflection symmetry if it can be divided into two identical halves by a line (axis of symmetry).
2. Rotational symmetry: An object has rotational symmetry if it looks the same after being rotated by a certain angle around its center.

We need to analyze each image and determine if it exhibits either type of symmetry.

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Images to Analyze:

1. Image (a): Butterfly
2. Image (b): Mango
3. Image (c): Umbrella
4. Image (d): Nose
5. Image (e): Smiley Face
6. Image (f): Tree

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Step-by-Step Analysis:

#### Image (a): Butterfly
- The butterfly has a clear vertical axis of symmetry. If you draw a vertical line down the middle, the left side mirrors the right side perfectly.
- Symmetry Type: Reflection symmetry
- Conclusion: Symmetrical

#### Image (b): Mango
- The mango does not have any obvious axis of symmetry. It is asymmetrical in shape, with one end wider than the other and an uneven distribution of features like the stem and curve.
- Symmetry Type: None
- Conclusion: Not symmetrical

#### Image (c): Umbrella
- The umbrella has a vertical axis of symmetry. If you draw a vertical line down the middle, the left side mirrors the right side perfectly.
- Symmetry Type: Reflection symmetry
- Conclusion: Symmetrical

#### Image (d): Nose
- The nose has a vertical axis of symmetry. If you draw a vertical line down the middle, the left side mirrors the right side perfectly.
- Symmetry Type: Reflection symmetry
- Conclusion: Symmetrical

#### Image (e): Smiley Face
- The smiley face has both vertical and horizontal axes of symmetry. It also has rotational symmetry because it looks the same when rotated by 180 degrees.
- Symmetry Type: Reflection symmetry and Rotational symmetry
- Conclusion: Symmetrical

#### Image (f): Tree
- The tree does not have a clear axis of symmetry. While some trees might appear somewhat symmetrical, this particular tree does not have a perfect mirror image on either side.
- Symmetry Type: None
- Conclusion: Not symmetrical

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Final Answer:

The symmetrical objects are:
- (a) Butterfly
- (c) Umbrella
- (d) Nose
- (e) Smiley Face

Boxed Answer:
\[
\boxed{a, c, d, e}
\]