Lesson 3: Isosceles Triangles

Question 4 • AZ-Geometry A (MA201)

Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure?

Answer

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

In an isosceles triangle, the two legs are equal. If the base angles were unequal, the larger base angle would be opposite one of those legs, and the smaller base angle would be opposite the other. Choice D says the side opposite the larger angle must be longer, contradicting that the legs are equal. Therefore, the base angles must have equal measure.

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