How many lines of symmetries are there in an equilateral triangle?a)0b)2c)3d)1Correct answer is option 'C'. Can you explain this answer?

Question

Answer

An equilateral triangle has three equal sides when we draw the lines of symmetry does should be three lines of symmetry...

Answer

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Answer

C

Answer

There are 3 lines of symmetry in an equilateral triangle.

Explanation:
An equilateral triangle is a triangle with three equal sides and three equal angles. It is also a regular polygon with three sides.

Symmetry refers to the balance and regularity of an object. In geometry, symmetry is the property of a shape that remains unchanged when it is rotated, reflected, or translated.

An equilateral triangle has three lines of symmetry, which are the lines that divide the triangle into two congruent halves. These lines are also known as axes of symmetry.

Here's an explanation of why there are three lines of symmetry in an equilateral triangle:

1. Vertical Line of Symmetry:
- A vertical line passing through the centroid of the triangle (the point of intersection of the medians) divides the triangle into two congruent halves.
- The centroid is the point of balance and is located at the intersection of the medians, which are the lines joining each vertex of the triangle to the midpoint of the opposite side.
- The vertical line passing through the centroid is a line of symmetry because the lengths of the segments from the vertices to the line are equal.

2. Line of Symmetry through Each Vertex:
- A line passing through each vertex of the triangle and the midpoint of the opposite side is a line of symmetry.
- Each of these lines divides the triangle into two congruent halves because the lengths of the segments from the vertices to the line are equal.

3. Line of Symmetry through Each Midpoint:
- A line passing through each midpoint of the triangle's sides and the midpoint of the opposite side is a line of symmetry.
- Each of these lines divides the triangle into two congruent halves because the lengths of the segments from the midpoints to the line are equal.

Therefore, an equilateral triangle has three lines of symmetry, which are the vertical line passing through the centroid, and the lines passing through each vertex and the midpoint of the opposite side, and the lines passing through each midpoint and the midpoint of the opposite side.

Answer

2

Answer

3

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