Triangle Inequality

Triangle Inequality

Given 3 sides determine if they can form a triangle ....

When you add the two shortest sides they must be longer than the longest side

Poll

Can a triangle have side lengths 5, 9, and 3?

• Yes

• No

Multiple Choice

Can a triangle have side lengths of 8, 8, and 8?

• Yes

• No

Given 2 sides of a triangle determine the range of possible lengths for the third side

Add the 2 numbers, Subtract the 2 numbers....the third side must be BETWEEN these 2 numbers (not equal to them!)

Multiple Choice

Two sides of a triangle have lengths of 8 inches and 6 inches. Which inequality represents the possible lengths of the third side?

• 2 > x > 14

• 2 < x < 14

• 6 < x < 8

• 6 > x > 8

Poll

Which of the following could be the length of the third side of a triangle with the other 2 sides being 3 and 7 (Select all)

• 3

• 4

• 7

• 8

• 10

Triangle Sum

The 3 angles of a triangle will always add to 180 degrees

Remember that an isosceles triangle has 2 equal sides and 2 equal angles

Multiple Choice

In triangle XYZ, the measure of angle X is 40 degrees and angle Y is 60 degrees. What is the measure of angle Z?

• 40

• 60

• 80

• 180

Open Ended

In the right triangle the lower left hand angle is 2x+1 and the lower right hand angle is 5x+5. Determine the value of x.

Multiple Choice

Solve for x.

• 8
• -10
• -7
• 6

Ordering side lengths when given angles

The shortest side is opposite the smallest angle

The longest side is opposite the largest angle

Multiple Choice

List the side measures in order, shortest to longest.

• QM, QP, MP
• MQ, MP, QP
• MP, MQ, QP

Multiple Choice

Identify the shortest side measure.

• QP
• QM
• MP

Ordering angle measures when given sides

The smallest angle is opposite the shortest side

The largest angle is opposite the longest side

Multiple Choice

Name the smallest angle in this triangle.

• ∠A

• ∠B

• ∠C

Multiple Choice

Name the largest angle in this triangle.

• ∠D

• ∠E

• ∠F

More Practice !!

Multiple Choice

Solve for x.

• 16
• 11
• 50
• 6

Multiple Choice

Can the sides of a triangle have lengths 3, 8, and 9?

• Yes
• No

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6?

• 6
• 7
• 5
• 4

Multiple Choice

Does a triangle with these side lengths exist?
15, 12, 9

• Yes
• No
• I don't know.

Multiple Choice

Where would the shortest side of a triangle be located?

• Across from the smallest angle in the triangle.
• Across from the largest angle in the triangle?
• Cannot tell.

Multiple Choice

What is a possible third side to a triangle with side lengths of 13 and 4?

• 9
• 12
• 8
• 5

Multiple Choice

The longest side of a triangle would be located where on a triangle?

• Across from the smallest angle
• Across from the largest angle
• Cannot tell.
• Adjacent to the smallest side.

Multiple Choice

Find the measure of the missing angle.

• 47

• 57

• 53

• 133