Pythagorean Converse

This is NOTES time

Get your notebook out. Write Pythagorean Theorem in it. Be ready to take notes.

Answer

a was a Pythagorean Triple because all 3 sides are whole numbers;


b was not a Pythagorean Triple because we got √147, which simplifies to 7√3, and not a whole number.

If you need more....

​Video on Canvas you can watch!

But Pythagorean Theorem can do MORE

When I have a right triangle, then a² + b² = c²


AND
when a² + b² = c², it proves I have a right triangle

Go back and look at that last slide again. Write it down

We can CLASSIFY triangles as acute or obtuse using Pyth Thm!!

I mean, wow. Who knew?

ALWAYS look at C. Is C² too big? it's obtuse. Is C² too small? It's acute.

​Here's my work.
Squaring a radical just removes the radical
Notice how I squared the 4√95. Square the 4 then square the radical, and multiply them together

Let's start with some easy ones

Multiple Choice

Name the longest side of a right triangle.

• leg a
• leg b
• leg 
• hypotenuse

Multiple Choice

What are the 2 shorter sides of a right triangle called?

• Hypotenuse
• Pythagorean Theorem
• Legs
• Right triangle

Multiple Choice

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

Multiple Choice

Do these 3 side lengths form a right triangle?
13, 80, and 81?

• yes
• no

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Now we're ready for the good stuff.

You can use a calculator to check, since they're not asking for your answer in simplest radical form. Just figure out which part is larger.

Multiple Choice

Given these side lengths, classify the triangle.

• Acute

• Obtuse

• Right

• Not a triangle

Multiple Choice

Given these side lengths, classify the triangle.

• Acute

• Obtuse

• Right

• Not a triangle

Multiple Choice

Given these side lengths, classify the triangle.

• Acute

• Obtuse

• Right

• Not a triangle

Multiple Choice

Given these side lengths, classify the triangle.

• Acute

• Obtuse

• Right

• Not a triangle

Multiple Choice

Which statement is the MOST accurate about the converse of the Pythagorean Theorem?

• The converse is used to determine an unknown side length.

• The converse is only useful with right triangles

• The converse is used to determine if a triangle is or is not a right triangle

• The converse always works out that a²+b²=c²

Check Canvas if you need more help. There's a video there.

You have a practice WS :)