If a triangle has at least two congruent sides, it is an isosceles triangle. an equilateral triangle has three congruent sides. which of the following is valid based on deductive reasoning? a. an isosceles triangle is an equilateral triangle. b. an equilateral triangle is an isosceles triangle. c. an isosceles triangle has three congruent sides. d. an equilateral triangle has two congruent sides.

B. An equilateral triangle is an isosceles triangle.

Step-by-step explanation:

We are given that if a triangle has atleast  two congruent sides , it is an isosceles triangle.

An isosceles triangle is that triangle in which two sides are congruent and two angles made by two congruent sides are congruent.

Now , we are given that an equilateral  triangle has three congruent sides .

We know that if a triangle is an equilateral triangle then it will have three congruent sides and three congruent angles.

If a triangle is an equilateral triangle then it will also an isosceles triangle because it is satisfied the property of an isosceles triangle.It means it will have two congruent sides and two congruent angles made by two congruent sides .Therefore, an equilateral triangle is an isosceles triangle.Hence, option B is true.

But

A. An isosceles triangle is an equilateral triangle . it is false because isosceles triangle have two congruent sides not three congruent sides therefore it can not be equilateral triangle. Hence, option A is false.

C. An isosceles triangle has three congruent sides.It is false statement because we know that  isosceles triangle have  only two congruent sides not three congruent sides. Therefore, option C is false.

D.An equilateral triangle has two congruent sides . It is false because we know that an equilateral triangle has three congruent sides not two.Therefore, option D is false.