5.5 use inequalities in a triangle

5.5

1. Solve 3x + 8 < 29.

ANSWER x < 7

ANSWER x > –122. Solve 15 > –2x – 9.

3. Solve 2x – 2 < (3x – 4) + (x – 8).

ANSWER x > 5

5.5 Use Inequalities in a TriangleBell Thinger

ANSWER 5, 6, 7, 8, 9, 104. Find all integer solutions for 4 < x < 11.

5. A triangle has angle measures 82° and 34°. Find themeasure of the third angle.

ANSWER 64°

5.5

5.5Example 1

Draw an obtuse scalene triangle. Find the largest angle and longest side and mark them in red. Find the smallest angle and shortest side and mark them in blue. What do you notice?

SOLUTION

The longest side and largest angle are opposite each other.

The shortest side and smallest angle are opposite each other.

5.5Example 2

5.5

SOLUTION

Draw a diagram and label the side lengths. The peak angle is opposite the longest side so, by Theorem 5.10, the peak angle is the largest angle.

The angle measures sum is 180 , so the third angle measure is 180 – (46 + 59 ) = 75 . You can now label the angle measures in your diagram.

o

o o o o

The greatest angle measure is 75 , so the correct answer is C.

o

Example 2

5.5Guided Practice

1. List the sides of RST in order from shortest to longest.

ST, RS, TRANSWER

5.5

Another stage prop is a right triangle with sides that are 6, 8, and 10 feet long and angles of 90°, about 37°, and about 53°. Sketch and label a diagram with the shortest side on the bottom and the right angle at the left.

2.

ANSWER

Guided Practice

5.5

5.5Example 3

ALGEBRA A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side.

SOLUTION

Let x represent the length of the third side. Draw diagrams to help visualize the small and large values of x. Then use the Triangle Inequality Theorem to write and solve inequalities.

5.5

Small values of x Large values of x

x + 8 > 12

x > 4

8 + 12 > x

20 > x,or x < 20

The length of the third side must be greater than 4 and less than 20.

ANSWER

Example 3

5.5Guided Practice

3. A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side.

4 < x < 26ANSWER

5.5Exit Slip

In Exercises 1 and 2, list the sides or angles in orderfrom least to greatest.

1.

ANSWER AB, BC, AC

5.5Exit Slip

In Exercises 1 and 2, list the sides or angles in orderfrom least to greatest.

2.

ANSWER ∠R, ∠T, ∠S

5.5Exit Slip

Tell whether the side lengths can form a triangle.

3. 37 m, 35 m, 18 m

ANSWER yes

4. 3 ft, 3 ft, 6 ft

ANSWER no

5.5Exit Slip

5. Jeremy wants to build a triangular toy using sticks.He has one stick that is 12 inches and another thatis 10 inches. What are the possible lengths of thethird side of the triangle?

ANSWER greater than 2 in. and less than 22 in.

5.5

Homework

Pg 345-348#8, 11, 14, 24, 33