Question

Can a triangle have a 60° angle and exactly two congruent sides? Explain.

Answer 1

No.

Explanation:

We are talking about an isosceles triangle with exactly two congruent sides.

We see that there are two cases:

First, the 60 degree angle may be the "lone angle" See below.

If 60 degree angle is the "lone angle", then the other two angles are congruent. Therefore,
`2theta+60=180`
`2theta=120`
`theta=60` which means that all of its sides are congruent to each other.

Second, the 60 degree angle may have its "twin" in the triangle. See below.

If 60 degree angle has its "twin", in the triangle, then the equation will look like this:
`60+60+theta=180`
`theta=60` which again gives an equilateral triangle.