Question

Consider the conjecture: An isosceles triangle is always equilateral

which are counterexamples that show the conjecture is false?
A.) An isosceles triangle with sides 6, 6, and 3.2
B.) An isosceles triangle with sides 4, 4, and 4
C.) An isosceles triangle with sides 5, 5, and 9
D.) An isosceles triangle with sides 5, 6, and 9.5
E.) An isosceles triangle with sides 4, 4, and 5.7​

Answer 1

A.) An isosceles triangle having the side lengths 6, 6, and 3.2.

C.) An isosceles triangle having the side lengths 5, 5, and 9.

E.) An isosceles triangle with sides 4, 4, and 5.7.

Explanation:

If we consider the conjecture: An isosceles triangle is always equilateral, then the followings are counterexamples that show the conjecture is false.

A.) An isosceles triangle having the side lengths 6, 6, and 3.2.

C.) An isosceles triangle having the side lengths 5, 5, and 9.

E.) An isosceles triangle with sides 4, 4, and 5.7.

Those triangles have two equal sides but the third sides are different. (Answer)