IM Commentary – The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry. A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections. A word has been added at the end of the solution about why there are not other lines of symmetries for these triangles: this has been inserted in case this topic comes up in a class discussion but the focus should be on identifying the proper lines of symmetry.

Contents

#### Does a triangle have exactly 3 lines of symmetry?

Yes, an equilateral triangle has exactly three lines of symmetry.

## What triangle has 3 lines of symmetry?

Equilateral triangle –

- An equilateral triangle has three lines of symmetry.
- It has rotational symmetry of order 3.
- It has three equal sides.
- All three angles are equal (60°)

## How do you count lines of symmetry?

Frequently Asked Questions on Line of Symmetry – What is the maximum number of lines of symmetry in an object? The number of lines of symmetry depends on the shape or figure. For example, an isosceles triangle has one line of symmetry, the rectangle has two lines of symmetry, and the circle has an infinite line of symmetry.

Are there shapes that have no lines of symmetry? The shapes or objects that are irregular and do not resemble each other when divided into two parts are called ASYMMETRIC. Such shapes do not have a line of symmetry. A scalene triangle, a parallelogram, and a trapezium are examples of shapes that have no lines of symmetry.

How do you find the line of symmetry for a shape? Fold the shape so that one half is identical to the other half. The line along which you have folded can be called a line of symmetry. There can be more than one such line or line of symmetry. How many lines of symmetry does a regular polygon have? In a regular polygon, all sides and angles are equal.

#### What shape has only 3 lines of symmetry?

An equilateral triangle has 3 lines of symmetry.

### What shapes have only 3 lines of symmetry?

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right. Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

This type of symmetry is called line symmetry, Any isosceles triangle has line symmetry. The dashed lines represent lines of symmetry, and each shape is said to be symmetrical about this line. The following all have line symmetry: A shape can have more than one line of symmetry. Thus a rectangle has two lines of symmetry, an equilateral triangle has three lines of symmetry, and a square has four. A circle has an infinite number of lines of symmetry since it can be folded about any diameter. Only eight of the possible lines of symmetry are indicated below. Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

#### Which triangle has no line of symmetry?

A scalene triangle is a triangle that has three unequal sides and hence it has no line of symmetry.

## What shape has 5 lines of symmetry?

A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides.

#### Which triangle has 1 line of symmetry?

Isosceles triangle has only one line of symmetry.

### Why can’t a triangle have 2 lines of symmetry?

Answer and Explanation: No, a triangle cannot have 2 lines of symmetry. The number of lines of symmetry a triangle can have depends on the type of triangle. Specifically, it’s the relationship between the three different sides of the triangle that determines its number of lines of symmetry.

### Which shape has 4 lines of symmetry?

A square has four lines of symmetry.

#### What is the symmetry of a triangle?

IM Commentary – The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry. A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced. For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections. A word has been added at the end of the solution about why there are not other lines of symmetries for these triangles: this has been inserted in case this topic comes up in a class discussion but the focus should be on identifying the proper lines of symmetry.

#### What shape has infinite lines of symmetry?

A circle has infinite many lines of symmetry.

## What shapes are not symmetrical?

Give three examples of shapes with no line of symmetry. Join Vedantu’s FREE Mastercalss Answer Verified Hint: To answer this question first we have to know about the line symmetry in geometric shapes. Then we will find out which shape has no line of symmetry. A parallelogram – A parallelogram has opposite sides equal and parallel but a parallelogram has no line of symmetry. A trapezium – In a trapezium, only two opposite sides are parallel to each other. A trapezium doesn’t have equal sides so it has no line of symmetry. So, we have a scalene triangle, trapezium, and a parallelogram with no line of symmetry. Note: Before solving this question a student must have a clear idea about line symmetry and rotational symmetry. Rotational symmetry is that a shape rotated around a point.

#### Can you draw a triangle with 2 lines of symmetry?

Can you draw a triangle, which has exactly two lines of symmetry? Sketch a rough figure. Join Vedantu’s FREE Mastercalss Answer Verified Hint: In this question, we have to draw a triangle, which has exactly two lines of symmetry. For this, we will draw three types of triangles based on sides, which are the scalene triangle, isosceles triangle, and equilateral triangle.

- After that, we will try to draw lines of symmetry of these triangles and check if any of them have exactly two lines of symmetry.
- Complete step-by-step solution Here, we have to draw a triangle, which has exactly two lines of symmetry.Let us first understand what a line of symmetry is.A line of symmetry is a line that cuts a shape exactly in half.

If we place a mirror along the line, the shape will remain unchanged.Based on this, we can draw three triangles based on their sides which are the scalene triangle, isosceles triangle, and equilateral triangle. Now, let us draw these triangles and their possible lines of symmetry.Scalene triangle: It is a triangle, which has all three sides different. As we can see, the scalene triangle has no line of symmetry. No line can cut this triangle into exactly two identical parts. So this is not our required triangle.Isosceles triangle: It is a triangle, which has two sides equal. (AB = AD in triangle ABC). As we can see, this triangle has only one line of symmetry. So, this is not our required triangle.Equilateral triangle: It is a triangle which has all sides equal. (AB = AC = BC in triangle ABC). As we can see, this triangle has exactly three lines of symmetry. So this is not our required triangle. Hence, there exists no triangle with exactly two lines of symmetry. Note: Students should take care that the line of symmetry creates two shapes which are mirror images of each other.

### Do 3D shapes have symmetry?

3D Symmetry – Similarly to 2D shapes, some 3D shapes are also symmetrical, Rather than having lines of symmetry, 3D shapes have planes of symmetry, A plane of symmetry occurs if you can cut the shape into two halves, the halves are mirror images of each other. We will look at the 3D symmetry of cylinders, prisms, and pyramids,

## Can a rectangle have 3 lines of symmetry?

Video Lesson on Properties of rectangles – A rectangle is a 4 sided polygon whose two opposite sides are equal and parallel. The angles of a rectangle are always 90 degrees and its diagonals are always equal. A rectangle has 2 lines of symmetry. The lines of symmetry in a rectangle cut its opposite sides into equal parts. Yes, a rectangle has rotational symmetry. A rectangle has rotational symmetry of 180° (Order 2). Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin! Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz Visit BYJU’S for all Maths related queries and study materials

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View Quiz Answers and Analysis : Lines of Symmetry in Rectangle (Definition and Order)

#### What is 3 fold symmetry?

3-fold Rotation Axis – Objects that repeat themselves upon rotation of 120o are said to have a 3-fold axis of rotational symmetry (360/120 =3), and they will repeat 3 times in a 360o rotation.

### Are scalene triangles symmetric?

Properties of A Scalene Triangle It has three angles of different measurements. It has no equal or parallel sides. Hence, there is no line of symmetry in a scalene triangle. It has no point symmetry or rotational symmetry.

#### Can you draw a triangle which has exactly no lines of symmetry?

Yes, we can make a scalene triangle which has no line of symmetry.

## Do triangles always have 3 vertices?

The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.

#### Does a triangle have 3 straight sides and 3 vertices?

Triangles – A triangle has 3 sides and 3 vertices (corners). A vertex is where two lines meet or join. There are different kinds of triangles. These triangles have sides that are all the same length. These triangles have sides that have two different lengths. Can you spot which sides are the same on each of the triangles? These triangles have sides that are all different lengths.