Unit 3 Algebraic Applications 8.9/8.14a

Pythagorean Theorem

By Dana Kuramoto

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​Learning Target:

I can ​model and apply the Pythagorean Theorem to find missing side lengths and hypotenuse lengths in right triangles. I can explain a proof of the Pythagorean Theorem and its converse.

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​Pythagorean Theorem Finding Hypotenuse and Missing Leg

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

What side(s) will always be the longest on a right triangle?

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Select

What side(s) will always be the shortest on a right triangle?

Select all that apply

• The Hypotenuse

• Leg A

• Leg B

• The Right Angle

Multiple Choice

The legs form what type of angle?

• Acute
• Obtuse
• Reflex
• Right

Multiple Choice

What is the relationship between the sides in the Pythagorean Theorem shown?

Hint: Think about when the hypotenuse is missing!

• a + b = c

• a² + b² = c²

• a² – b² = c²

• a – b = c

-Miss Issa

Watch the videos on the next slide to help you answer the questions after. Make sure to take notes! Have a paper, pencil, and DESMOS ready to answer the practice questions after.

Multiple Choice

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

• 6

• 6.7

• 3

• 15.7

• None of them

Multiple Choice

_{^{Find the missing side}}

• 9
• 41
• 6.4
• 6.2

Fill in the Blanks

Multiple Choice

 A hot air balloon is tied to the ground by a 200yd rope as shown in the picture below. The balloon is floating 20 yds west of where the rope is tied to the ground. About how high in the air is the hot air balloon?

• 205
• 199
• 220
• 400

Multiple Choice

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Multiple Choice

Which equation is verified by the following graphic?

• $$3+4=5$$  

• $$3^{2\ }+\ 4^{2\ }=\ 5^2$$  

• $$3^2+5^2=4^2$$  

• $$4^2+5^2=3^2$$  

Multiple Choice

Find the length of the missing side. 

• 25 cm
• 42 cm
• 52 cm
• 48 cm

Multiple Choice

What is the formula used to solve for the hypotenuse?

• a² + b² = c²

• a + b = c

• a - b = c

• a² + b² + c²

Multiple Choice

Calculate the missing side

• 37

• 17.66

• 6

• 312

Multiple Choice

Calculate the missing side

• 9

• 26.9

• 37

• 18.2

Multiple Choice

Calculate the missing side

• 9

• 41

• 6.4

• 3

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

Multiple Choice

Look at the following image. Which could be used to determine if the following is a right triange?

• $$5^2-12^2=13^2$$

• $$5^2+12^2=13^2$$

• $$12^2-5^2=13^2$$

• $$5^2+12^3=13^4$$

Multiple Choice

Which of the measurements form a right triangle?

• 10cm, 24cm, 26cm

• 9cm, 12cm, 18cm

• 17cm, 23cm, 40cm

• 5cm, 7cm, 10cm

Multiple Select

Select the lengths below that would construct a right triangle.

• 3, 4, 5

• 8, 15, 17

• 5, 12, 14

• 3, 4, 7

Multiple Choice

Given the following lengths of the sides of a triangle, which of the following is not a right triangle?

• 10, 12, 15

• 3, 4, 5

• 5, 12, 13

• 6, 8, 10

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

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Multiple Choice

What is the diagonal length of the iPad?

• 9.2 in
• 11 in
• 13 in
• 9.6 in

Multiple Choice

Which equation is modeled by the picture shown?

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

Multiple Choice

Solve for the walkway length

• 30
• 40
• 58
• 35

Multiple Choice

What is the formula used to solve for the hypotenuse?

• a²⁺b²=c²
• a+b=c
• a-b=c
• c-a=c

Multiple Choice

A model of the Pythagorean Theorem is shown. Which statement is true?

• If you add the areas of regions R and P they will add to the area of region Q

• If you add areas of regions R and Q they will add to the area of region P

• If you subtract the areas of regions Q and R they will make the area of region P

8.14a
Evaluating Expressions

Multiple Choice

Evaluate the expression:

$$6^2-4\div2$$  

• 4

• 34

• 16

• 10

Multiple Select

In the order of operations, which one comes first?

• Exponents

• Addition

• Multiplication

Here is the order of operations

What does left to right mean on M/D and A/S?

Let's dive in and start evaluating some expressions!

The next several slides are numeric expressions. Remember: to evaluate a numeric expression you use the order of operations to simplify it to a single value.

Multiple Choice

Evaluate the expression.

$$6\cdot2^2+3$$  

• 42

• 27

• 67

• 142

Multiple Choice

Evaluate the expression.

$$\left(8-5\right)\cdot12+3^2$$  

• 54

• 42

• 63

• 45

Multiple Choice

Which student correctly used the order of operations while solving this problem?

Let's take a look at algebraic expressions now!

The next slides are algebraic expressions. Remember: to evaluate an algebraic expression, start by substituting in the value of the variable. Then follow the order of operations to simplify to a single number.

Some algebraic expressions have more than one variable!

Just substitute in both variable values at the beginning of the problem.

Multiple Choice

Evaluate $$a-5-b$$ when a = 4 and b = 10. 

• 1

• -9

• -11

• 9

Multiple Choice

Evaluate $$\frac{16+2x}{y+1}$$ when x = -2 and y = -4 

• -4

• 5

• 2

• -6

Multiple Choice

Evaluate the expression.   Let g = 3    h = 9 
4h + 2g + 4

• 42
• 46
• 34
• 58

Multiple Choice

evaluate bc + 5a  
when  a = 3, b = 4, and c = -6

• 9
• 38
• -38
• -9