Question

Name a triangle which has exactly one line of symmetry. Show line of symmetry in figure.

Answer 1

Hint: This question is based on Geometry. In this question we have to determine the type of triangle which has exactly one line of symmetry and then we have to draw that type of triangle. A line of symmetry is an imaginary line and this line passes through the centre of the drawing and divides the drawing into two identical half drawings. The line of symmetry is represented by the dotted line.

Complete step-by-step answer:
Given:
Let us construct a triangle $ \Delta ABC $ in such a way that its two sides AB and BC are equal and two inner angles $ \angle A $ and $ \angle C $ are equal.
So, we have
In $ \Delta ABC $ ,
 $ AB = BC $
And,
 $ \angle A = \angle C $
Also drawing a vertical dotted line XY passing through the centre of the triangle O. This dotted line is the “line of symmetry”. This line intersects base of the triangle AC at a point D in such a way that –
 $ \Delta ACD \equiv \Delta BCD $
It means that the two triangles $ \Delta ACD{\text{ and }}\Delta BCD $ formed on the both sides of the line of symmetry XY are identical.
This type of triangle, which has two equal sides, two equal angles and exactly one line of symmetry is known as the Isosceles Triangle.
So, $ \Delta ABC $ is an Isosceles Triangle.
Therefore, the triangle which has only one line of symmetry has been known as the Isosceles Triangle.

Note: In an isosceles triangle which has all three sides equal is known as the Equilateral Triangle. This triangle is a special case of the isosceles triangle. So, if in an equilateral triangle all three sides are equal then all three angles of the triangle would be equal too.