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The Pythagorean Theorem

- By
- Melissa Selby

Review Parts of a triangle

Hypotenuse- The longest side of a triangle.

Hypotenuse

Legs

Legs The two shortest sides of a triangle.

Pythagorean Theorem

- The square of the hypotenuse is equal to the

squares of the legs of the triangle. - Used only on right triangles.

Formulain terms of variables

ABC

C

A

B

Examples

A2, B2.5, C?

- Lets label the parts.

C?

A 2

B 2.5

Original formula ABC

C?

A 2

B 2.5

22.5C 46.25C 46.2510.25 10.25C

ñ10.25ñC 3.20 C

Common Mistakes

- When you get to the end of your problem and you

have something like - 125C
- Do not forget to take the square root of both

sides

Common Mistakes

- Always round to the nearest hundredth
- 1.25576188999 1.26

Common Mistakes

- vs.
- When you round use
- not
- Why?

Other ways to write the Pythagorean Theorem

- B²C²-A²
- And
- A²C²-B²

How did we get them?

- Original A²B²C²
- Subtract A from both sides
- -A²A²B²C²-A²
- New formula! B²C²-A²

How did we get them?

- Original A²B²C²
- Subtract B from both sides
- -B²A²B²C²-B²
- New formula! A²C²-B²

Lets make them harder!

A3 B? C5

- Which version of the Pythagorean theorem should

we use? - 1.) A²B²C²
- 2.) B²C²-A²
- 3.) A²C²-B²
- 2.) B²C²-A²

A3 B? C5

- Label the parts

C5

A3

B?

B²5²-3²

- B²25-9
- B²16
- vB² v 16
- B4

A? B8 C10

- Which version of the Pythagorean theorem should

we use? - 1.) A²B²C²
- 2.) B²C²-A²
- 3.) A²C²-B²
- 3.) A²C²-B²

A? B8 C10

- Label the parts

C10

A?

B8

A²10²-8²

- A²10²-8²
- A²100-64
- A²36
- vA² v 36
- A6

Word Problem!!!

The story of

Rapunzel and Her Prince

My way

Rapunzel

Prince Charming

Castle

Rapunzel and her prince charming have a new

problem.Rapunzel cut her hair! Now Prince

Charming cant reach her.What is he going to

do!?!

It will be o.k. sweetheart. Ill figure it out

Oh no!

Well, lucky for Rapunzel her Prince Charming is a

rich engineer.Prince charming knows he just

needs the measurements of the building and his

ladder.Can you help him find the height of the

castle?

Each line is one hundred feet

Now we need to know how long Prince Charmings

ladder is.

Each step is one hundred and ten feet from the

last one.

What do we want to know?

How far from the bottom of the castle does Prince

Charming need to put his ladder?

What do we know?

- The ladder is 1,210 feet from the ground to the

top step. - The castle is 1,000 feet tall

Lets make it a right triangle.

Cladder

Acastle

B?

Put it in a formula.

- B²C²-A²
- A1000 B? C1210
- B²1210²-1000²
- B²1464100-1000000
- B²464100
- v B² v 464100
- B681.24885
- round
- B681.25

So, how far from the bottom of the castle does

prince charming need to put his ladder?

681.25 Feet

Review

Do the work on your paper

A16 B12 C?

- 35
- 64
- 22
- 20
- Dont cheat!

Sorry that is incorrectLets work through the

problem

- 16²12²C²
- 256144C²
- v 400 v C²
- 20C

Try again

Correct!Go to the next problem

A? B15 C32

- 30.33
- 28.27
- 29.25
- 55.55

Sorry that is incorrectLets work through the

problem

- 32²-15²A²
- 1024-225A²
- v299vA²
- 28.27A

Correct!

The end

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