Download Geometry 5-7 Triangle Inequalities

Name _________________________ Class _____________ Date _____________
5-7 Geometry Practice – Inequalities in Triangles
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.
3.
2.
4.
5.
6. ∆XYZ, where XY = 25, YZ = 11, and XZ = 15
For Exercises 6–8, list the sides of each triangle in order from shortest
to longest.
7.
8.
9. ∆MNO, where m∠M = 56, m∠N = 108, and m∠O = 16
10. List the sides in order from shortest to longest in ∆XYZ, with
m∠X = 50, m∠Y = 5x + 10, and m∠Z = 5x.
Can a triangle have sides with the given lengths? Explain.
11. 10 in., 13 in., 18 in.
12. 6 m, 5 m, 12 m
13. 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.
14. 4, 8
15. 13, 8
16. 10, 15
17. A student draws a triangle with a perimeter of 12 in. The student says that the
longest side measures 7 in. How do you know that the student is incorrect?
Determine which side is shortest and which side is longest in the diagram.
18.
19.
20. A student draws a triangle with a perimeter 36 cm. The student says that the longest side
measures 18 cm. How do you know that the student is incorrect? Explain.
21. Which side is longer, JL or MO? Write an inequality relating the two sides.
22. List the sides in order from shortest to longest in ∆ABC, with m∠A = 80, m∠B = 3x + 5,
and m∠C = 5x − 1.