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5:4 Inequalities for Sides and Angles of a TrianglePowerPoint Presentation

5:4 Inequalities for Sides and Angles of a Triangle

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### 5:4 Inequalities for Sides and Angles of a Triangle

Objective: Recognize and apply relationships between sides and angles of triangles

EX.

7

12

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.

B

A

9

List the angles from greatest

to least.

D

35°

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.

55°

E

F

List the sides from shortest

to longest.

EXAMPLE

- Which is greater, mCBD or mCDB?
- Is mADB> mDBA?
- Which is greater, mCDA or mCBA?

C

15

D

16

8

12

A

10

B

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

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

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

100º

40º

C

B

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