Question

which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure?
the base angles of an equilateral triangle have equal measure.
if two sides of a triangle are equal, the third side must be equal to the others.
if a triangle is equiangular, then it is equilateral.
if one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Explanation:

The isosceles triangle theorem (base angles equal) relies on the converse of the triangle inequality related to angle-side relationships. The correct fact is the angle-side inequality: if one angle is larger, its opposite side is longer, which implies equal sides correspond to equal opposite angles.

Answer:

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.