Geometry
Chapter 5.5 Inequalities for Sides and Angles of a Triangle
Name _________________________
Chapter 5 Day 6
Objective: After studying this lesson, you should be able to:

Recognize and use relationships between sides and angles in a triangle.
What is your conclusion?
In a triangle, the longest side is across from ___________________________________________
In a triangle, the smallest angle is across from ___________________________________________
#1 Identifying largest and smallest sides and angles in triangles.
1) In triangle ABC, m<A = 30° and m<B = 80°. Arrange the sides from least to greatest.
2) Given right triangle ABC, arrange the angles in order from least to greatest.
#2 Identifying largest and smallest sides and angles in triangles on a coordinate plane.
1)RST has coordinates R(0, -3), S(-3, 4), and T(-1, 2).
a. Draw RST on the coordinate plane.
b. Determine the lengths of the sides of the
triangle using the distance formula. Arrange the
lengths from smallest to largest.
c. Arrange the angles from smallest to largest.
d. Verify your findings with a protractor.
#3 Identifying largest and smallest sides and angles in triangles algebraically.
1) In JKL , KL = 13x + 6, JL = 8x + 5 and JK = 7x – 7. List the angles of JKL in order from least to
greatest if the perimeter of JKL is 144 feet.
2) In PQR , mP  6 x  4, mQ  7 x  12, and mR  6 x  7 . List the sides of PQR in order from the
longest to the shortest.
#4 Identifying largest and smallest sides and angles in triangles using geometric reasoning
1) In triangle ABC, m<C = 55°, and m<C > m<B. Which is the longest side of the triangle?
For problems 2-6 use the figure at the right.
2) Which side of PAT is the longest?
3) Which side of HPT is the shortest?
4) Arrange the sides of PAT in order from least to greatest.
5) Arrange the sides of HPT in order from least to greatest.
6) What is the longest side in the entire figure?
Homework
Level 1: Identifying largest and smallest sides and angles in triangles.
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H
E
C
F
B
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G
A
D
#2 Identifying largest and smallest sides and angles in triangles on a coordinate plane.
2) IJK has coordinates I(6, 2), J(-4, -1), and K(-2, 3).
a. Draw IJK on the coordinate plane.
b. Determine the lengths of the sides of the
triangle. Arrange the lengths from smallest to
largest.
c. Arrange the angles from smallest to largest.
d. Classify the triangle according to its sides and angles.
#3 Identifying largest and smallest sides and angles in triangles algebraically.
3) List the angles of KLM in order from least to greatest if KL = x – 4, LM = x + 4, KM = 2x – 1 and
the perimeter of KLM is 27.
4) In LMN, mL = x2–10x, mM = x+75, mN = –3x+77. List the possible sides of LMN in order
from the longest to the shortest.
#4 Identifying largest and smallest sides and angles in triangles using geometric reasoning
5) Name the least angle in ABC .
6) Name the greatest angle in ABC .
7) Name the least angle in BCD .
8) Name the greatest angle in BCD .
9) Find the shortest segment in the figure. Hint – put the sides of each triangle in order from least to
greatest first. (This figure is not drawn to scale.)