8th Grade Lesson 11/8/2021

8th Grade Lesson 11/8/2021

by Kevvin Hankins

Understanding & Applying the Pythagorean Theorem

MGSE.8.G Standards:

• Understand and apply the Pythagorean Theorem.

• MGSE8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

• MGSE8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

• MGSE8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

I will be able to:

• Identify the parts of a right triangle to explain the proof of the Pythagorean Theorem

• Find the missing measurement of a right triangle using the Pythagorean Theorem in mathematical problems in two and three dimensions

• Apply the Pythagorean Theorem to real-world problems in two and three dimensions

Pythagorean Theorem

Pythagorean Theorem & It's Converse

October 11th, 2021

Right Triangle Parts

• The 2 shorter sides that make up the RIGHT ANGLE are the "LEGS a & b"

• The LEGS can be in any order that makes up the RIGHT ANGLE

• The longest side is the "HYPOTENUSE c"

• The HYPOTENUSE is OPPOSITE from the RIGHT ANGLE

The Pythagorean Theorem Formula

a² + b² = c²

Why the Pythagorean Theorem Formula

a² + b² = c² works:

• In Right Triangles, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c)

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

Example Problem #1

Solve to find the missing measurement: HYPOTENUSE

Steps to Solve for the HYPOTENUSE (c)

• Use the Pythagorean Theorem Formula a² + b² = c²

• Substitute the values for Legs a and b into the formula

• Square each number

• Add the values for a and b

• Find the square root for both sides of the equal sign

Example Problem #2

Solve to find the missing measurement: LEG a or b

Steps to Solve for the LEG (a or b)

• Use the Pythagorean Theorem Formula a² + b² = c²

• Substitute the values for Leg a or b and the Hypotenuse c into the formula

• Square each number

• Subtract the values for a or b from c

• Find the square root for both sides of the equal sign

Multiple Select

What is the formula for the Pythagorean Theorem?

• c² = a² + b²

• a³ + b³ = c³

• a² + b² = c²

• c³ = a³ + b³

Multiple Choice

What are the parts of the right triangle called that make up the right angle?

• Right Angle

• Hypotenuse

• Legs

• Pythagorean Theorem

Multiple Choice

What is the part of the right triangle called that is opposite of the right angle?

• Right Angle

• Hypotenuse

• Legs

• Pythagorean Theorem

Multiple Choice

Find the missing value in the right triangle. Round your answer to the nearest tenth if necessary.

• 12.8 ft

• 10 ft

• 6 ft

• 8 ft

Multiple Choice

Find the missing value in the right triangle. Round your answer to the nearest tenth if necessary.

• 1.4 ft

• 10 ft

• 5.3 ft

• 3.7 ft