PROBLEM SET
THEOREMS ON TRIANGLE INEQUALITIES
(Triangle Inequality, Exterior Angle Inequality, Hinge and its Converse)
A. Encircle the angle which has the greatest measure.
1) \( \angle 6, \angle 5, \angle 1 \)
6) \( \angle 12, \angle 9, \angle 14 \)
B. Tell whether a triangle can be constructed with segments having the following lengths.
1) \( 6,8,13 \)
3) \( 8.4,6.3,2.3 \)
5) \( x, y, x-y( \) where \( x>y) \)
2) \( 11,9,15 \)
4) \( 6,1,4 \)
C. Two sides of a triangle have the following measures. Find the range of possible measures for the third side.
1) 6 and 10
2) 9 and 5
3) 14 and 11
5)
D. Write an inequality relating the given pairs of angle and segment measures.
1) \( R T \) \( \qquad \) AC
2) \( C D \) \( \qquad \) AD
3)
4) \( m \angle P Q S \) \( \qquad \) \( m \angle R Q S \)
5) \( \mathrm{m} \angle \mathrm{FHE} \) \( \qquad \) \( \mathrm{m} \angle \mathrm{FHG} \)