Chapter 8, Problem 1MC

To determine

Whether the statement “Any triangle, right or oblique, can be solved if at least one side and any other two measures are known” is true or false.

Answer to Problem 1MC

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

In a triangle, if one measure is a side, then the other two possible measures are side and side, side and angle, angle and angle.

If two possibilities are sides, then triangle has three sides. That is, SSS.

If three sides are known, then will draw triangle.

If two possibilities are angles, then triangle has one side and two angles. That is, AAS.

If one side and two angles are known, then will draw triangle.

If two possibilities are angles, then triangle has one side and two angles. That is, ASA.

If one side and two angles are known, then will draw triangle.

If two possibilities are one angle and one side, then triangle has one side and two angles. That is, SAS.

If one angle and two sides are known, then will draw triangle.

If two possibilities are one angle and one side, then triangle has one side and two angles. That is, SSA.

If one angle and two sides are known, then will draw triangle.

Therefore, the statement “Any triangle, right or oblique, can be solved if at least one angle and any other two measures are known” is $\underset{\_}{\text{true}}$.