Understanding & Applying the Pythagorean Theorem

Understanding & Applying the Pythagorean Theorem

MAFS.8.G.2.6

MAFS.8.G.2.7

MAFS Standards:

•  MAFS.8.G.2.6 Explain a proof of the Pythagorean Theorem and its converse. 

•  MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 

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

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)

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

Multiple Choice

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

• 6.5 cm

• 6.4 cm

• 4.7 cm

• 2.5 cm

Multiple Choice

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

• 41.6

• 41.7

• 29.3

• 29.2