Question

justifying the isosceles triang
which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles 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.
the base angles of an equilateral triangle have equal measure.
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 focuses on the relationship between sides and angles in a triangle. The fact "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" is a fundamental property related to triangle side - angle relationships. An isosceles triangle has two equal sides. By the converse of the mentioned property (if two sides are equal, then the angles opposite them are equal), we can prove the isosceles triangle theorem.
The first option "If two sides of a triangle are equal, the third side must be equal to the others" is incorrect as it would describe an equilateral triangle, not just an isosceles one. The second option "If a triangle is equiangular, then it is equilateral" is about equiangular - equilateral relationship, not directly relevant to proving the isosceles triangle theorem. The third option "The base angles of an equilateral triangle have equal measure" is about a specific case (equilateral triangle which is a special case of isosceles) but not a general proof - aiding fact for the isosceles triangle theorem.

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.