Question

If possible, draw
A. An obtuse – angled equilateral triangle
B. A right – angled equilateral triangle
C. A triangle with two right angles.

Answer 1

Hint: In this question we have to draw a particular given requirement if it is possible. The given requirements are based on triangles, so by using some triangle property, we can draw the required diagram. The sum of all the angles of a triangle is \[{180^ \circ }\]. This property is known as angle sum property. If the triangles satisfy this condition, then we can draw the given triangles.

Complete step-by-step solution:
We have to draw:
A. An obtuse – angled equilateral triangle
An obtuse – angled equilateral triangle
We can’t draw an obtuse angled equilateral triangle, because an obtuse angle has a measurement greater than ${90^ \circ }$ but less than ${180^ \circ }$. We know that, sum of angles in a triangle is ${180^ \circ }$ and the triangle to equilateral all the sides should be equal and all the corresponding angles also should be equal. So, it is not possible to draw obtuse angled equilateral triangles.
B. A right – angled equilateral triangle
A right – angled equilateral triangle
Similarly, we can’t draw an right angled equilateral triangle, because a right angle has a measurement ${90^ \circ }$. We know that, sum of angles in a triangle is ${180^ \circ }$ so other angles will be in the measurement between ${1^ \circ } - {45^ \circ }$. Also, we already know that, to equilateral all the sides should be equal and all the corresponding angles also should be equal. So, it is not possible to draw a right angled equilateral triangle.
C. A triangle with two right angles
A triangle with two right angles:
It is not possible to draw a triangle with two right angles.
We know that the sum of all the angles of a triangle is \[{180^ \circ }\]. If the two angles are right angles, then the sum of those angles is \[{180^ \circ }\]. There will not be a third angle. So, we cannot draw any triangle.

Note: We have to remember that, in Mathematics, an obtuse angle is an angle which is greater than ${90^ \circ }$ and less than \[{180^ \circ }\].
An obtuse – angled equilateral triangle means any one angle of a triangle is obtuse and the side adjacent to the angle is equal.
A right – angled equilateral triangle means any one angle of a triangle is the right angle and the side adjacent to the angle is equal.