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.

Answer 1

Fact 4.

Proof (contradiction): Let triangle ABC have AB = AC. Suppose ∠B ≠ ∠C. Without loss of generality assume ∠B > ∠C. By fact 4, the side opposite the larger angle is longer, so AC > AB. That contradicts AB = AC. Hence ∠B = ∠C, so the base angles are equal.