Side Lengths of Triangles

Open Ended

What is something you used to be scared of but aren't anymore?

Triangle Inequality Theorem

Standard:

MA.8.GR.1.3 Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.

Triangle Inequality Theorem

I can calculate the missing side length of a triangle when given two sides using the Triangle Inequality Theorem.

Multiple Choice

Recall:

Find the measure of the missing angles.

• A

• B

• C

• D

Here are the rules about triangles:

• ALL angles need to add up to be 180 degrees! No matter what!

• The 3rd side of a triangle needs to be smaller than the sum of your two shorter sides.

• If you do not meet either of these rules, IT ISN'T A TRIANGLE!

Example:

I have the sides 2 ft, 2 ft, and 4 ft.

Add your two shortest sides: 2 + 2

2 + 2 is 4. Is my third side smaller than 4?

NO! This will not be a triangle. A good option for a 3rd side could be 3 ft or 2 ft. 4ft is too wide!

Open Ended

I Do:

My triangle has these side lengths:

6 ft, 7ft, 8ft

Is this a triangle?

Draw

We Do:

Determine if it is possible to form a triangle with the given side lengths. 7 yd, 8 yd, 9 yd

Multiple Select

We Do:

If a triangle has shorter side lengths of 12 cm and 14 cm, which of the following could not be the 3rd side length?

Select all that apply.

• 27 cm

• 23 cm

• 42 cm

• 30 cm

Draw

You Do:

Do the following side lengths form a triangle?
2 inches, 2 inches, 5 inches.

SHOW YOUR WORK.

Multiple Select

Let's review:

Triangles need:

• Angles that will add up to equal 180 degrees

• Angles to equal 90 degrees

• Third side to be BIGGER than the sum of your two smallest sides.

• Third side to be SMALLER than the sum of your two smallest sides.

Multiple Choice

Exit Ticket:

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

• I don't know.

• Cannot be determined