Question

is possible to draw the following triangles? Give reason
(iii)An obtuse angled equilateral triangle (iv)/An equilateral triangle with each angle 70*


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Answer 1

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If possible, draw

A. An obtuse – angled equilateral triangle

B. A right – angled equilateral triangle

C. A triangle with two right angles.

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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∘

. 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∘ but less than 180∘. We know that, sum of angles in a triangle is 180∘ 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∘. We know that, sum of angles in a triangle is 180∘ so other angles will be in the measurement between 1∘−45∘. 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∘

. If the two angles are right angles, then the sum of those angles is 180∘

. There will not be a third angle. So, we cannot draw any triangle.