Does it Look the Same? Class 5 Notes Maths Chapter 5

Symmetry

• Any Object (Shape, letter or number) that can be divided or folded into two equal halves along a straight line is said to show Symmetry.
• One half of the symmetrical shape is the mirror image of the other.
• Example: Here given both the objects look identical on either side of the line drawn through it.
  

Example 1: Name any two alphabets which possess symmetry?

Alphabet (A), (H) possess symmetry.

Example 2: Can you give any two real objects which possess symmetry?

Leaf, Lungs in our body possess symmetry.

Line of Symmetry: 

• The line that divides a figure into two equal halves is called the line of symmetry. 
• When a figure is folded in half along its symmetry line, the two parts perfectly match.
• For example, we have a tree given here, which we may fold/divide into two equal parts.
  
• The importance of Line of Symmetry is to make a symmetrical figure, we simply draw the mirror image of the given figure along the line of symmetry. 

Example 3: Draw the mirror image of the given figure keeping the line of symmetry in mind.

Below given figure shows the full image of the above figure. By using the line of Symmetry concept we have drawn the mirror image of the given half which resulted in the full image.

Types of Symmetry: 

• There are two types of symmetry. They are (a) Vertical Symmetry and (b) Horizontal Symmetry
• Vertical Symmetry: A vertical line of symmetry is that line which runs down an image thus dividing it into two identical halves.
  
• Horizontal Symmetry: A horizontal line of symmetry is that line that runs across the image thus dividing into two identical halves.
  
• Observing the number of lines of Symmetry: Symmetrical figures can have more than one line of symmetry. The below image shows examples of different number lines of symmetry.
  

Asymmetric

• Any Object (Shape, letter or number) that cannot be divided or folded into two equal halves (or) the two sides of any objects are different when compared is called Asymmetric.
• In Asymmetric one half is not a mirror reflection of the other.
• Check out the below image to see the difference between the Symmetry and Asymmetry.
  

Combination of Symmetry and Asymmetry 

• Objects can be both symmetric and asymmetric, which means even though the shape is Symmetric, the colour scheme/any other difference of the figure can make it Asymmetric. 
• For example, here we can observe that with respect to the shape they are symmetric but according to the colour they are asymmetric.
  

Rotation of Shape: 

• When a shape turns clockwise or anticlockwise around a fixed spot the size and the shape itself will remain the same, but its position in space will change.
• Clockwise Direction: It is the same direction as the hands on the clock.
  
• Anti clock Direction: It is the opposite direction in which the hands of a clock move.
  
• Half Turn: A rotation by 180 degrees (or) 2 right angles (each right angle is 90 degrees) is known as a half turn.
  
• Quarter Turn: A rotation by a right angle i.e, 90 degrees is known as a quarter turn. It is also known as the one-fourth Turn.
  
• The relation between half a turn and a quarter turn is that 2 quarter Turns  = 1 half turn.
  
• One-Sixth Turn: When an object rotates either clockwise or anticlockwise from point A to point B then we say that the object completed one-sixth rotation.
  

Example 4: Write any 5 examples of 5 digit numbers which look the same on half a turn?

Give below are the examples 5 digit numbers that look the same on half a turn

• 10001
• 10801
• 16091
• 16891
• 19061

Example 5: Can you find out the turns in the patterns shown in the figure.

If you clearly observe the diagram it has done one-fourth turn. We all know one-fourth turn is nothing but 90 degrees rotation. Let's apply one-fourth turn to the given alphabet and observe whether it matches the given image or not.
On applying the one-fourth turn we will get the turns in the below image form.

Hence the answer is one-fourth turn.

Patterns

• Patterns are repeated arrangements of shapes, colours and numbers which are arranged while rotating it. We can create patterns by rotating shapes.
• There are different patterns that we can observe in our daily life, For example, floor pattern, wall patterns, design patterns of sarees, dress shirts etc.,
• Rules to Create Patterns: We can make three different rules to turn it clockwise and can create the pattern.
  • Rule I: Repeat it with a one-fourth turn
  • Rule II: Repeat it with a half-turn
  • Rule III: Repeat it with a three-fourth turn.