8.G.B.3-Squaring Up: Proving the Pythagorean Theorem-notes/lesso

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right

90

hypotenuse

legs

longest

Right Triangles

- Have a 90 degree angle

- The side across from the right angle is called the hypotenuse. It is the longest side

- The other two sides are called legs

Labelling

Label the missing parts of the triangle:

Drag labels to their correct position on the image

Hypotenuse

Leg

Labelling

Drag the correct letter to the box.

Drag labels to their correct position on the image

B

A

C

Labelling

Label the sides of the right triangle

Drag labels to their correct position on the image

Base

Height

Hypotenuse

Labelling

Label the parts of this right triangle with their appropriate name.

Drag labels to their correct position on the image

Hypotenuse

Leg b

Leg a

RIGHT

hypotenuse

legs

a²

b²

c²

Triangle F

Triangle A

Multiple Choice

Which equation is the Pythagorean Theorem?

• $$a^2+b^2=c^2$$

• $$a+b=c$$

Triangle D

Today we will:

Be able to figure out if a triangle is a right triangle by checking if its side lengths fit the Pythagorean Theorem

Multiple Choice

Which equation is the Pythagorean Theorem?

• $$a^2+b^2=c^2$$

• $$a+b=c$$

The Pythagorean Theorem

• For ALL right triangles, the Pythagorean Theorem applies

The Pythagorean Theorem

• For ALL right triangles, the Pythagorean Theorem applies

• How can we use the Pythagorean Theorem to figure out if a triangle is a right triangle or not, given the side lengths?

Practice

We will determine if triangles ARE or ARE NOT right triangles

Triangle A

Triangle B

Triangle C

Triangle D

Multiple Choice

Triangle E
Leg lengths: 5 and 9
Hypotenuse length:  $$\sqrt{100}$$

• This IS a right triangle

• This IS NOT a right triangle

Triangle F

Triangle G

Triangle H

Multiple Choice

Triangle J
Leg lengths: 4 and 7
Hypotenuse length:  $$\sqrt{65}$$

• This IS a right triangle

• This IS NOT a right triangle

squares

largest

reasoning

Multiple Choice

Which equation is modeled by the picture shown?

• 3²+5²=4²
• 3²+4²=5²
• 5²+4²=3²
• 9²+16²=25²

Multiple Choice

What is the area of the third square?

• 6.7 cm²
• 33.5 cm²
• 2025 cm²
• 45 cm²

Multiple Choice

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

• 12 in²
• 144 in²
• 194 in²
• 13.9 in²

Multiple Choice

If 231 square feet of paint was used to paint the two squares blue, how much paint would be needed to paint the white square purple?

• 15.2 ft²
• 115.5 ft²
• 231 ft²
• 10.7 ft²

Multiple Choice

If the area of square a is 45 in² and the area of square b is 65 in², what is the area of square c?

• 20 in²
• 100 in²
• 79.1 in²
• 110 in²

Multiple Choice

If c² is 625 cm² and b is 24 cm, what is the length of a?

• 25.4 cm
• 24.5 cm
• 7 cm
• 26 cm

Multiple Choice

If the area of square b is 144 ft² and the length of side a is 5 ft, what is the area of square c?

• 169 ft²
• 13 ft²
• 12.2 ft²
• 10.9 ft²

Multiple Choice

If the area of square c is 1,369 cm² and the area of square b is 1,225 cm², what is the length of one side of square a?

• 12 cm
• 144 cm
• 50.9 cm
• 8.5 cm

Multiple Choice

If a = 5 and b = 7, what is the area of square c?

• 74
• 8.6
• 12
• 6241

Multiple Choice

What is the length of the three sides of the right triangle shown?

• 10,26,36
• 10,24,26
• 26,96,100
• 10,26,28

Multiple Choice

Which of the following sentences would belong in the proof that describes this image?

• The sum of the areas of the two smaller squares is equal to the area of the large square.
• The sum of the side lengths of the two smaller squares is equal to the side length of the large square.
• The difference of the areas of the two smaller squares is equal to the area of the large square.
• The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

Multiple Choice

The total sum of areas a and b is equal to the area of c

• True 
• False

Multiple Choice

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

The legs form what type of angle?

• Acute
• Obtuse
• Reflex
• Right

Multiple Choice

What is the opposite of squaring a number?

• divide
• multiply 
• fractions
• square root

Multiple Choice

The Pythagorean Theorem is
a² + b³ = c⁴

• false
• true

Multiple Choice

All of the a square plus all of the b square will perfectly fill the c square with nothing left over.

• True

• False

Multiple Choice

Who is is?

• some man

• Sponge Bob

• Pythagoras

a²

c²

RIGHT

c

NOT

b²

Multiple Choice

Which of the following forms a right triangle?

• A

• B

• C

• D

Multiple Choice

Which set of sides would make a right triangle?

• (9,12,21)
• (8,10,12)
• (9, 12, 15)
• (5,10,15)

Math Response

Find the value of x. Round your answer to the nearest tenth.

Type answer here

Correct Answer: 20.9

Deg^°

Rad

Math Response

Find the value of x.

Type answer here

Correct Answer: 10

Deg^°

Rad

Dropdown

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.

How many miles is the road from the mall to her house?

Select answer

​

What is her total distance traveled?

Select answer

​

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

missing

classify

construction

navigation

Multiple Choice

In order to use the Pythagorean Theorem to finding a missing side length:

• the triangle must be a right triangle

• it can be any type of triangle

• the triangle must be an acute triangle

• the triangle must be an obtuse triangle

Multiple Choice

Triangle LMN has side lengths of 20 ft, 12 ft, and 16 ft. Use the Converse of the Pythagorean Theorem to determine whether or not the triangle is a right triangle.

• Yes

• No

Fill in the Blanks

Multiple Choice

Which equation will help you find the missing side?

• $$4^2+10^2=c^2$$

• $$10^2-4^2=c^2$$

• $$c^2=100+10^2$$

• $$c^2+4^2=10^2$$

Multiple Choice

What is the formula for Pythagorean theorem?

• a²⁺b²=c²
• a+b=c
• a-b=c
• c-a=c

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

• 9
• 40
• 41

Multiple Choice

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

• Hypotenuse
• Pythagorean Theorem
• Legs
• Right triangle

Multiple Choice

A soccer field is a rectangle that measures 90 meters wide and 120 meters long. The coach asks the players to run from one corner to the other corner, diagonally across the field. How far do the players have to run?

• 150 meters

• 210 meters

• 180 meters

• 135 meters

Multiple Choice

What is the length of a diagonal of a 10 cm by 15 cm rectangle?

• 18 cm

• 17 cm

• 25 cm

• 22.36 cm