Question

Which statement is always true, based on the Venn diagram? If a triangle is equilateral, then the triangle must also be isosceles. If a triangle is isosceles, then the triangle must also be equilateral. If a triangle is isosceles, then the triangle will never also be equilateral. If a triangle is equilateral, then the triangle will not always be isosceles.

Answer 1

A. If a triangle is equilateral, then the triangle must also be isosceles.

Explanation:

According to the Venn Diagram,

We see that, the bigger circle represents the set of isosceles triangles and the smaller circle represents the set of equilateral triangles.

Since, the smaller circle is completely contained in the bigger circle.

Therefore, all the elements of the set of equilateral triangles belong to the set of isosceles triangles.

This implies that 'if a triangle is equilateral, then the triangle must be isosceles'.

So, among the four options provided, first option is correct.

Answer 2

because the orange circle for Equilateral triangles is inside the blue circle for isosceles triangles:

If a triangle is equilateral, then the triangle must also be isosceles.