Download Inequalities in One Triangle

Name
5-5
Class
Date
HW
Inequalities in One Triangle
1. Explain the relationship of m∠1, m∠2, and m∠3.
The measure of an exterior angle of a triangle is
than the measure of each of its remote
angles.
∠1 is an
angle of the triangle, so m∠1 >
and m∠1 >
.
For Exercises 2–5, list the angles of each triangle in order from smallest to
largest.
2.
3.
4. ∆XYZ, where XY = 25, YZ = 11, and XZ = 15 (hint: Draw triangle XYZ; label the sides)
For Exercises 6–8, list the sides of each triangle in order from shortest
to longest.
5.
6.
7. ∆MNO, where m∠M = 56, m∠N = 108, and m∠O = 16 (hint: Draw triangle MNO; label
the sides)
8. Algebra List the sides in order from shortest to longest in ∆XYZ, with m∠X
= 50, m∠Y = 5x + 10, and m∠Z = 5x.
Name
5-5
Class
Date
HW (continued)
Inequalities in One Triangle
Can a triangle have sides with the given lengths?
8. 10 in., 13 in., 18 in.
9. 6 m, 5 m, 12 m
10. 11 ft, 8 ft, 18 ft
The lengths of two sides of a triangle are given. Find the range of possible
lengths for the third side.
11. 4, 8
12. 13, 8
13. 10, 15