Pythagoras: step-by-step

Pythagoras: step-by-step

Steps to success, this guy was a pretty big deal!

The most important part of the process: label your sides!!

• The longest side (opposite the right angle) is the hypotenuse. We call this "c" in the pythagarean formula.

• The other two sides are often called legs. They are the smaller sides and are adjacent to the right angle.

Multiple Choice

35 is the longest side of the triangle and it is called the hypotenuse

• True

• False

Multiple Choice

What is the hypotenuse of the triangle P?

• q

• r

• p

• p and q

Multiple Choice

The shortest leg of the triangle measures

• 16

• 30

• 34

• 16 and 30

Multiple Choice

The hyopotenuse of the triangle measures

• 32

• 24

• 40

• 32 and 24

Multiple Choice

The hypotenuse of the following triangle measures

• 28

• 23

• $\sqrt{28}$

• $\sqrt{23}$

Multiple Choice

What is the longest side of a right triangle called?

• Adjacent

• Opposite

• Hypotenuse

• Arm

Why does it work?

• https://www.youtube.com/watch?v=dxyti_wCWaE&ab_channel=missnorledge

• This is a visual explanation of the reason it works!!

Got it? Let's practice.

If the squares on the smaller sides are 16cm² and 9cm², what must the square on the hypotenuse equal?

Multiple Choice

What is the area of the blue square?

• 36cm²

• 64cm²

• 100cm²

• 10cm²

Multiple Choice

What is the area of the yellow box?

• 110cm²

• 100cm²

• 84cm²

• 36cm²

Open Ended

Why does this work? Write your answer.

Let's look at the steps to find the hypotenuse...

• Step 1: LABEL YOUR TRIANGLE!

• In this example, x would be c.

Let's look at the steps to find the hypotenuse...

• Step 2: Decide what needs to be done, addition or subtraction?

• If you are trying to find the hypotenuse, you will need to ADD the squares of the sides together.

Let's look at the steps to find the hypotenuse...

• Step 3: complete the calculation and square root the answer!

• For this triangle, I will find the squares of both 17.3m and 22.8m. Then I can add these together. Finally, I need to square root to find the answer.

Multiple Choice

Find the length of c to the nearest hundredth.

• 11.00

• 9.95

• 8.06

• 3.32

Multiple Choice

_{^{Find the missing side}}

• 9
• 41
• 6.4
• 6.2

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Multiple Choice

what is the missing length?

• 50

• 60

• 70

• 80

Multiple Choice

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles
• 32 miles
• 37 miles
• 40 miles

How about a missing side?

What about a missing smaller side?

• Step 1: LABEL YOUR SIDES!

• In this example, 19cm would be the hypotenuse and therefore is "c"

What about a missing smaller side?

• Step 2: Decide on your calculation.

• In this example, I am trying to find the smaller side. Remember SSS!! Smaller Side Subtract. I will need to subtract to find the smaller side.

What about a missing smaller side?

• Step 3: Do the calculation and square root!

• Square 19cm and 14cm. Then 19cm squared minus 14cm squared. Finally, square root the answer!!

Multiple Choice

Find x.

• 35
• 20
• 8
• 12

Multiple Choice

What is the value of x?

• √666
• √216
• √441
• √225

Multiple Choice

Find the length of b in this triangle.

• 31
• 36
• 60
• 62