Question

In each of the following state if the statement is true or false:
Every acute triangle is equilateral.

Answer 1

Hint: Before answering this question let us see what an equilateral triangle is and what is the meaning of an acute angle. As we know, a triangle in which all sides, angles and vertex are equal are called equilateral triangles.It is also known as equiangular triangle because all of its angles are equal to $ {60^ \circ } $ .

Complete step-by-step answer:
We have been given a statement i.e. Every acute triangle is equilateral.
We know that an acute angle is a kind of angle that measures between $ 0 $ to $ {90^ \circ } $ or we can say that an angle whose measure is less than $ {90^ \circ } $ is known as acute angle. Such angles are $ {45^ \circ },{30^ \circ },{60^ \circ }... $ and so on.
Now from the above definition we can see that an equilateral triangle has to be the angle of $ {60^ \circ } $ . It cannot be less than that of acute angles.
So the equilateral triangle has an acute angle but not every acute triangle is equilateral.
Hence the above given statement is false.
So, the correct answer is “False”.

Note: We should note that each acute triangle is not an equilateral triangle but each equilateral triangle is an acute triangle. So we can say that a triangle in which all the three angles measures less than $ {90^ \circ } $ is called an acute triangle with non-identical sides and measures. And the sum of all the angles is always equal to $ {180^ \circ } $ .