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Section 5.5 Notes – Geometry
Inequalities in Triangles
Name: _____________________________
Period: _________
Goal: Be able to use inequalities involving angles of triangles and sides of triangles.
Theorem: The _____________ side of a triangle is opposite the ______________ ____________.
Theorem: The _____________ angle of a triangle is opposite the _____________ ____________.
Directions: List the angles or sides of each triangle in order from smallest to largest.
1.
2.
Directions: Determine which segment is shortest.
3.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is ______________ than the length of the 3rd side.
Directions: Can a triangle have sides with the given lengths? Explain.
4.
5. 18, 32, 21
Directions: The lengths of two sides are given. Describe the lengths for the possible third side.
6.
5 and 11
7.
21 and 27
8. List sides in order from shortest to longest in ABC if mA 10x, mB  5x 17, and mC  7x 1
9. List angles in order from shortest to longest in ABC if AB  3x 18, BC  5x  3, and AC  7x 12
when the perimeter is 108.
Exterior Angle Inequality Theorem
The measure of an exterior angle is _______________ than the measure of each of its remote interior
angles.
10.
Find m1
Recap:
11a. Explain why m4  m1.
11.
11b. Explain why m3  m1.
11c. Use ABC to describe the possible lengths of AC .
12. Can a triangle have length of 2, 3, and 6?
13. In XYZ, XY  5, YZ  8, XZ  7 . Which angle is the largest?
14. In PQT, mP  50 and mT  70 . Which side is the shortest?
Directions: List the side lengths in order from longest to shortest of the following triangles.
15.
17.
16.
If 54 and 58 are the lengths of two sides of a triangles, what are the possible lengths of the third
side of the triangle?
18. What is wrong with this picture?
Directions:
19.
Find the measure of the indicated angles.
20.