1. 5:4 Inequalities for Sides and Angles of a Triangle
Objective: Recognize and apply relationships between sides and angles of triangles

2. C
Theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
EX. 7 12 A B 9
List the angles from greatest
to least.

3. EX: D
Theorem: If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
35°
55° E F
List the sides from shortest
to longest.

4. EXAMPLE Which is greater, mCBD or mCDB? C Is mADB> mDBA? D
Which is greater, mCDA or mCBA? C 15 D 8 12 16 A 10 B

5. PRACTICE Name the angle with the least measure in ▲LMN.
Which angle in ▲MOT has the greatest measure?
Name the greatest of the six angles in the two triangles, LMN and MOT. L 10 N 7 6 M 9 5 O 8 T

6. EXAMPLE 1. Which side of ▲RTU is the longest?
2. Name the side of ▲UST that is the longest. 3. T
30º
110º R U S

7. PRACTICE 1. What is the longest segment in ▲CED?
2. Find the longest segment in ▲ABE.
3. Find the longest segment on the figure. Justify your choice.
4. What is the shortest segment in BCDE?
5. Is the figure drawn to scale? Explain. A E
55º D
50º
30º
40º
100º C B

8. Exit Ticket
Find the value of x and list the sides of ∆ABC in order for SHORTEST to LONGEST if the angles have the indicated measures.
m∠A = 12x - 9, m∠B = 62 – 3x ,
m∠C = 16x + 2