Question

By drawing a free hand sketch of the following, draw the line (s) of symmetry:
an isosceles right-angled triangle

Answer 1

Hint: We have to draw a line of symmetry for an isosceles right-angled triangle as per the requirement. In order to draw it, we have to first draw two sides equal so that an isosceles triangle is formed. After this, we will draw a line originating from the common vertex of both the sides which cuts the third side into half. This line will be called the line of symmetry.

Complete step-by-step answer:
A right triangle with two equal length legs is known as an isosceles right triangle. The corresponding angles will be congruent since the two legs of the right triangle are equal in length. Two legs and two acute angles are thus congruent in an isosceles right triangle.
The axis or imaginary line that passes through the middle of the shape or object and splits it into equal halves is known as the line of symmetry.
Let us draw line of symmetry in case of an isosceles right-angled triangle:
Step One: Draw a triangle with two sides equal i.e. an isosceles triangle with one angle as right angled
In\[\vartriangle ABC\], \[AB = BC\]and \[m\angle B = {90^ \circ }\]

Step Two: Draw a straight line originating from the common vertex of both the equal sides i.e. vertex \[B\]and bisecting \[\overline {AC} \]in two equal parts at point \[D\]as follows:

Here \[AD = DC\]and \[\overline {BD} \]is the line of symmetry as it cuts the third side of the triangle into two equal halves.

Note: I.In order to draw \[m\angle B = {90^ \circ }\], we generally use scale or ruler. Since we have to draw a free hand sketch, we have to use a compass/rounder and draw it with the help of arcs.

II.In case of an isosceles triangle, there can be only one line of symmetry. There can be no other line which can cut this triangle into two equal halves. Moreover, in case of a scalene triangle, there are no lines of symmetry whereas an equilateral triangle has three lines of symmetry.