It is possible to have a right-angled equilateral triangle. State whether the statement is true or false.

Solution:

Given, it is possible to have a right-angled equilateral triangle.

We have to determine if the given statement is true or false.

A right angle is an angle that measures 90 degrees.

In a right angled triangle, one angle is equal to 90 degrees.

Consider a triangle ABC,

By angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

∠A + 90° + ∠C = 180°

∠A + ∠C = 180° - 90°

∠A + ∠C = 90°

An equilateral triangle is a triangle that has all its sides equal in length.

The three angles of the equilateral triangle are congruent and equal to 60 degrees.

Therefore, it is not possible to have a right-angled equilateral triangle.

✦ Try This: It is possible to have a right-angled acute triangle. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 76

It is possible to have a right-angled equilateral triangle. State whether the statement is true or false.

Summary:

The given statement,”It is possible to have a right-angled equilateral triangle” is false.

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