Is the triangle shown here an isosceles triangle?

Explanation

We will consider the measures of the angles of the triangle.  If two angles of a triangle are congruent, then the sides opposite the angles have the same length, and the triangle is isosceles.

∠ A and ∠ B have the same measure, 50°.

By the converse of the isosceles triangle theorem, if

m(∠A) = m(∠B), we know that m(BC) = m(AC) and that △ABC is isosceles.