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5.5 – Use Inequalities in a Triangle

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Page 1: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

5.5 – Use Inequalities in a Triangle

Page 2: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

M N

P

Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your triangle.

2.9cm 5.4cm

6.5cm56º 26º

98º

Page 3: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Theorem:

If one side of the triangle is longer than the other side, then the angle opposite the longer side is larger than the angle opposite the shorter side

Page 4: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Theorem:

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Page 5: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

1. List the sides and angles in order from smallest to largest.

Sides Angles

C

A

AB

BC

AC B

Page 6: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Sides Angles

R

S

1. List the sides and angles in order from smallest to largest.

ST

RT

SR T

Page 7: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

55°

1. List the sides and angles in order from smallest to largest.

Sides Angles

H

J

KJ

KH

JH K

Page 8: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

33°

1. List the sides and angles in order from smallest to largest.

Sides Angles

E

D

DF

EF

DE F

Page 9: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Construct a triangle with sides of 2, 2, and 6 cm.

2cm

6cm

Doesn’t work!

Why?

Page 10: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

6cm

2cm

Too short!

2cm

What if I tried 3, 3, and 6cm?

Page 11: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

6cm3cm 3cm

Still doesn’t work!

Page 12: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Triangle Inequality Theorem:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

a

b

ca + b > c

a + c > b

b + c > a

Page 13: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

2. Can a triangle be formed with sides 1, 2, and 5?

No, 1 + 2 > 5

Page 14: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

2. With 6, 7, and 11?

Yes, 6 + 7 > 117 + 11 > 66 + 11 > 7

Page 15: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

2. With 8, 12, and 20?

No, 8 + 12 > 20

Page 16: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

x + 9 > 21 x + 21 > 921 + 9 > xx > 12 30 > x

orx < 30

x > -12

12 < x < 30

3. What are the restrictions on x?

Page 17: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

Trick!

Subtract the two sides to find the lowest and add to find the highest.

Page 18: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

3. What are the possible values for the third side of a triangle with sides 9 and 12?

12 – 9 <

3 < x < 21

x < 12 + 9

Page 19: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

5. What are the possible values for the third side of a triangle with sides 14 and 20?

20 – 14 <

6 < x < 34

x < 20 + 14

Page 20: 5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your

6. Solve the inequality AB + AC > BC for x.

3x + 1 + 4x – 2 > 5x + 7

7x – 1 > 5x + 7

2x – 1 > 7

2x > 8

x > 4


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