Triangle Inequalities

Triangle Inequalities

Side and Angle Relationships

Poll

Can you make a triangle with any 3 side lengths?

• Yes

• No

Triangle Inequality Theorem states that the sum of any two side lengths of a triangle is greater than the third side length.

• In other words, add the two smallest side lengths of a triangle and compare it to the third side length. If the sum is greater than the third side length, then yes a triangle is possible if not then a triangle is not possible.

• For example, 7, 15, 17 makes a triangle since 7 + 15 > 17

• For example, 1, 2, 3 does not make a triangle since 1 + 2 is not greater than 3.

Can the following sets of side lengths make a triangle?

• 7, 8, 13

• 5, 5, 5

• 6, 14, 7

• 2, 6, 4

Multiple Select

Which of the following sets of side lengths will make a triangle?

• 7, 15, 17

• 8, 12, 16

• 3, 5, 10

• 4, 5, 10

• 22, 11, 11

Determining the possible values for a third side length of a triangle given two of the side lengths.

• First calculate the difference of the two given side lengths

• Second calculate the sum of the two given side lengths

• Combine the two values as a compound inequality, for example difference < x < sum

Open Ended

What is the range of values for x?

Open Ended

What is the range of values for x?

Multiple Choice

What is the range of possible values for x?

• 6 < x < 12

• 3 < x < 9

• 6 < x < 9

• 3 < x < 12

Multiple Choice

What is the range of possible values for x?

• 2.8 < x < 5.4

• 1.3 < x < 4.1

• 2.8 < x < 4.1

• 1.3 < x < 5.4

Ordering a Triangle's Angle measures given its Side Lengths

• The smallest angle is across from the shortest side.

• The largest angle is across from the longest side.

Open Ended

Which angle is the smallest?

Which angle is the largest?

Order the angles from least to greatest.

Open Ended

Which angle is the smallest?

Which angle is the largest?

Order the angles from least to greatest.

Multiple Choice

Order the angles from least to greatest.

• A, B, C

• C, B, A

• B, A, C

• B, C, A

Multiple Choice

Order the angles from least to greatest.

• A, B, C

• B, A, C

• A, C, B

• C, A, B

Ordering a Triangle's Side Lengths given its Angle Measure

• Shortest side will be across the smallest angle.

• Longest side will be across the largest angle.

Open Ended

Which side is the shortest?

Which side is the longest?

List the sides from least to greatest.

Open Ended

Which side is the shortest?

Which side is the longest?

List the sides from least to greatest.

Multiple Choice

Order the sides from least to greatest.

• AB, BC, CA

• BC, AB, CA

• AB, AC, BC

• CA, AB, BC

Multiple Choice

Order the sides from least to greatest.

• BC, AC, AB

• AB, AC, BC

• AC, AB, BC

• BC, AB, AC