Definition Types of Symmetry Lines of Symmetry and Solved Examples
Geometry and Symmetry
Geometry and Symmetry do not sound like photographic techniques more than the sort of things you would study from a math book.
Mathematically, symmetrical shapes are beautiful, powerful compositional tools that make images stand out from the crowd. Geometry and symmetry are two techniques that work better when combined. Both are powerful compositional tools in their own terms. Both Geometry and symmetry are found in nature as well as in man-made worlds when combined in one single shot can lead to some fantastic images. In this article we will discuss symmetry geometry, what are geometry and symmetry, Meaning of symmetry in Mathematics, etc.
Meaning of Symmetry in Geometry
In symmetry Geometry, an object has symmetry if there is an operation or transformation (such as rotational, reflection or translation) that represents a figure or objects to its original shape. Hence, symmetry geometry can be defined as the immunity to change. For example, a circle when rotated about its center will have a similar shape and size as the original circle as all the points of the circle after and before transformation would be indistinguishable. Hence, a circle in geometry is said to be symmetric under rotation or rotational symmetry.
What are Geometry and Symmetry?
Let's study about geometry and symmetry in photography.
Symmetry is drawn when either the bottom, top, left or right diagonals are mirror images of each other. Symmetry by its definition enables you to think outside of the rule of thirds'.
Symmetry even feels unnatural to seasoned photographers to use a center point to define your composition. Although symmetry occurs in nature, it is quite more visible in the man-made world.
Geometry is the Science of Different Shapes.
Square,line of triangles and circle all are geometrical elements that can be used in geometry. We can make use of hard-edge geometrical shapes to design bold imagery or more subtle "soft-edged" geometry to define a composition.
Both geometry and symmetry do not have to be restricted to physics. Lights and shapes can also have geometrical shapes and manifest symmetry.
Symmetry in Mathematics.
In Mathematics,symmetry is defined that one shape will exactly look like another shape when it is flipped, turned or rotated. For example, if you draw the heart shape in a paper and cut out from a piece of paper, design one - half of the heart at the fold and cut it to find the other half exactly similar to the first half. The heart extracted is an example of symmetry
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The definition of symmetry in Maths states that 'symmetry pictures in Maths is a mirror image'.When an image exactly looks like the original image after it has been turned or flipped then it is known as symmetry.
Symmetry Picture in Maths
Here, we will discuss symmetry pictures in Maths.
We know that symmetrical pictures in Maths may have one or more than one line of symmetry.
Some symmetrical pictures in maths have one line of symmetry, two lines of symmetry or infinite lines of symmetry.
The symmetrical shapes given below having one line of symmetry
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The symmetrical shapes given below have two lines of symmetry.
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The symmetrical shape given below having three lines of symmetry.
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The symmetrical shape given below having four lines of symmetry.
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The Symmetrical shape given below has an infinite line of symmetry.
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Solved Examples
1. The Picture Given Below is the Half Part and its Line of Symmetry. Complete the Picture Below.
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Solution:
The complete picture of the figure given in the questions is given below:
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The other part of the picture should be the same as the given half. We can use the grids to find the other part of the picture.
2. Which of the Figures Given Below Does not have a Line of Symmetry?
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Solution:
If we wrap both the papers from top to down as shown in figure A1 and B1, we find a line of symmetry in figure A but not in figure B. If we wrap both the papers from left to right as shown in figure below A2 and B2, we will not find any line of symmetries in both A and B.
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Quiz Time
1. Which of the Following Letters Below has no Line of Symmetry
U
H
S
A
2. How Many Lines of Symmetry are there in a Scalene Triangle?
3
0
2
1
3. What Letter Given Below Looks the Same after Reflection when the Mirror is Placed Vertically?
H
Q
P
S
Fun Facts
The line of symmetry is also known as the mirror line or axis of symmetry.
Infinite lines of symmetry are there in a circle.
FAQs on Figures With Symmetry in Geometry
1. What are figures with symmetry in maths?
A figure with symmetry is a shape that can be divided or transformed so that one part exactly matches another part. In geometry, symmetry means the figure remains unchanged after a reflection, rotation, or flip.
- If a shape can be folded into two equal halves, it has line symmetry.
- If it looks the same after turning around a fixed point, it has rotational symmetry.
- Common symmetric figures include squares, circles, rectangles, and equilateral triangles.
2. What is line symmetry?
Line symmetry is when a figure can be divided into two identical mirror-image halves by a straight line. This line is called the line of symmetry.
- If you fold the shape along the line, both halves match exactly.
- A square has 4 lines of symmetry.
- An isosceles triangle has 1 line of symmetry.
3. What is rotational symmetry?
Rotational symmetry occurs when a figure looks the same after being rotated about a fixed point by a certain angle less than 360°. The number of times a figure matches itself in one full turn is called its order of rotational symmetry.
- A square has rotational symmetry of order 4.
- An equilateral triangle has order 3.
- A circle has infinite order of rotational symmetry.
4. How do you find the line of symmetry of a shape?
To find the line of symmetry, check whether a shape can be folded into two identical mirror-image halves. Follow these steps:
- Fold the shape (mentally or physically) along a possible line.
- See if both halves overlap exactly.
- Count all such lines that divide the shape equally.
5. What is the difference between line symmetry and rotational symmetry?
The main difference is that line symmetry involves reflection across a line, while rotational symmetry involves turning around a point.
- Line symmetry: Shape matches after folding along a line.
- Rotational symmetry: Shape matches after rotating by a certain angle.
- A square has both line symmetry (4 lines) and rotational symmetry (order 4).
6. How many lines of symmetry does a circle have?
A circle has infinitely many lines of symmetry. Any line passing through the center divides the circle into two equal halves.
- Every diameter is a line of symmetry.
- The circle also has infinite rotational symmetry.
7. How many lines of symmetry does a square have?
A square has 4 lines of symmetry. These lines divide the square into equal mirror-image halves.
- 2 lines pass through the midpoints of opposite sides (vertical and horizontal).
- 2 lines pass through opposite vertices (diagonals).
8. What is the order of rotational symmetry?
The order of rotational symmetry is the number of times a figure matches itself during a full 360° rotation. It is calculated by checking how many positions look identical in one complete turn.
- Order = 360° ÷ smallest angle of rotation.
- For a regular pentagon, order = 5.
- For a rectangle (not a square), order = 2.
9. What are some examples of figures with symmetry?
Common figures with symmetry include regular polygons and basic geometric shapes. Examples are:
- Equilateral triangle – 3 lines of symmetry, rotational order 3.
- Square – 4 lines of symmetry, rotational order 4.
- Rectangle – 2 lines of symmetry, rotational order 2.
- Circle – infinite lines of symmetry and infinite rotational symmetry.
10. Why is symmetry important in geometry?
Symmetry is important in geometry because it helps identify shape properties, classify figures, and solve problems more easily.
- It simplifies calculations in constructions and proofs.
- It is used in coordinate geometry and transformations.
- It appears in real-life applications like architecture, art, and design.
