Question

Which criteria determine more than one triangle?

A side lengths of 8 cm, 15 cm, and 17 cm

B angle measures of 60°, 60°, and 60°

C two given angle measures of 48° and 72° and an included side measure of 50 in.

D two given side measures of 18 cm and 14 cm and an included angle measure of 52°

Answer 1

Answer: B

Explanation:

Let's analyze each option:

A) We know all the sides:

Ok, if we know all the sides, we can make only one triangle with it, so this defines only one triangle:

B) We know only the angles, all the angles are the same so this is an equilateral triangle, now we can make infinity equilateral triangles if we change the length of the side, so this criterion makes more than one triangle.

C) We have two angles (so we basically have 3 angles, because all the angles of a triangle must add up to 180°) and one side, so the other two sides are defined already, with this we can make only one triangle.

D) Two sides and one included angle (meaning that this angle goes between the two known sides)

With this, we already can find the missing side and then the complete triangle, so this criterion only defines one triangle.