Answer:
only 3 lines of symmetry does an equilateral triangle have.
Explanation:
Since a triangle can have 3 or 1 or no lines of symmetry.
In a equilateral triangle:
*All sides are equal
*All angles are equal i.e each of 60 degree.
Symmetry is when there is an exact replica or reflection of a shape or a line.
Line of symmetry: It is an imaginary line that runs through the center of a line or shape creating two perfectly identical halves.
A line of symmetry for a given triangle must go through each vertex as shown in figure;
Therefore, the equilateral with 3 sides equal has 3 lines of symmetry.
An equilateral triangle has [tex]\fbox{\begin\\\ 3\text{lines}\\\end{minispace}}[/tex] of reflection symmetry.
Further explanation:
A triangle is a two dimensional closed figure which is formed when three non-collinear points are joined. There are three sides, three angles and three vertices of a triangle.
On the basis of sides and angles triangles are classified as follows:
1) Scalene triangle: A triangle in which all the sides and the angles have a unique value is called a scalene triangle.
2) Isosceles triangle: A triangle in which any two sides or two angles are equal then the triangle is called an isosceles triangle.
3) Equilateral triangle: A triangle in which all the sides and the angles are equal then the triangle is called an equilateral triangle.
A line of reflection is defined as a line across which the image of a figure or an object is reflected.
The reflected image is of same size as of the original image.
In case of an equilateral triangle if we drop a median from one of the vertex of the triangle to its opposite side then it is observed that the median divides the equilateral triangle into two equal halves.
From figure 1 (attached in the end) it is observed that the median AD of an equilateral trinagle [tex]\triangle \text{ABC}[/tex] divides the triangle into two equal halves.
As per the above statement it is concluded that the median AD is the line of reflection symmetry for the equilateral triangle [tex]\triangle \text{ABC}[/tex].
Now, similarly if we drop a median form the vertex B or C to its opposite side then it is observed that the triangle into two equal halves.
Figure 2 (attached in the end) shows that the median dropped from the vertex B and C divides the triangle into two equal halves.
This implies that the median BD and CD are also the line of reflection symmetry for the equilateral triangle ABC.
So, the total number of lines of reflection symmetry for an equilateral triangle is [tex]3[/tex].
Thus, an equilateral triangle has [tex]3[/tex] lines of reflection symmetry.
Learn more:
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3. Inverse function https://brainly.com/question/1632445
Answer details
Grade: High school
Subject: Mathematics
Chapter: Triangles
Keywords: Triangle, isosceles, scalene, equilateral, angles, vertex, non-collinear, reflection, symmetry, line of reflection, line of symmetry, median, reflected image.
