Geometry Notes
5.5 Use Inequalities in One Triangle
Name _______________
If one side of a triangle is longer than
If one angle of a triangle is larger than
another side, then the angle opposite the
another angle, then the side opposite the
longer side is larger than the angle opposite
larger angle is longer than the side opposite
the shorter side.
the smaller angle.
List the angles in order from smallest to largest.
1.
2.
3.
List the sides in order from longest to shortest.
4.
5.
Can any group of segments be used to form a triangle? Look at the three attempts below.
What would have to happen in the last two attempts to make a complete triangle?
Triangle Inequality Theorem:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
6.
Is it possible for the side lengths of triangles to have the following measures?
3 cm, 5 cm, 4 cm
7.
17 in, 17 in, 34 in
8.
6 m, 50 m, 39 m
Describe the possible side lengths for the third side of a triangle given two sides.
9.
6 in and 9 in
10.
5 in and 5 in
11.
9 m and 18 m
PRACTICE, PRACTICE, PRACTICE!
List the sides of the following figure in order from shortest to longest.
12.
13.
14. Describe the possible values of x.
15. If m ! A = 5x+2, m ! B = 6x – 10, m ! C = x + 20, list the sides of ! ABC in order from
longest to shortest.
16. In ! KLM, KL = x - 4, LM = x + 4, KM = 2x – 1, and the perimeter of the triangle is 27.
List the angles of the triangle in order from least to greatest.