In triangle ABC, the length of side AB is 8. If the measure of ∠A and the measure of ∠B are equal, which of the following is NOT a possible length of side BC?
Question
In triangle ABC, the length of side AB is 8. If the measure of ∠A and the measure of ∠B are equal, which of the following is NOT a possible length of side BC?
Solution
The triangle ABC is an isosceles triangle because the measures of ∠A and ∠B are equal. In an isosceles triangle, two sides are of equal length. Therefore, the lengths of sides AB and AC are equal, which is 8.
The length of side BC can be any value between 0 and 16 (exclusive) according to the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
So, any value equal to or greater than 16 or equal to or less than 0 is NOT a possible length of side BC.
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