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List the angles and sides of each triangle in order from smallest to largest.
SOLUTION: Based on the diagram, we see that By Theorem 5.9, the measure of the angle opposite the longer side has a greater measure than the angle opposite the shorter side, therefore Angle: Side:
SOLUTION: By the Triangle Angle-Sum Theorem, Therefore, by Theorem 5.10 we know that the side opposite the greater angle is longer than the side opposite a lesser angle and Angle: Side:
List the angles and sides of each triangle in order from smallest to largest.
SOLUTION: Using the Triangle Angle-Sum Theorem, we can solve for x, as shown below.
degrees, degrees and the degrees.
Therefore,. By Theorem 5.10, we know that the lengths of sides across from larger angles are longer than those across from shorter angles so. Angle: P , Q , M Side: SENSE-MAKING Use the figure to determine the relationship between the measures of the given angles.
- BFD, BDF SOLUTION: The side opposite is , which is of length 12. The side opposite is , which is of length 15. Since by Theorem 5.9.
- DBF, BFD SOLUTION: The side opposite is , which is of length 5. The side opposite is , which is of length 12. Since by Theorem 5.9.
