Exploring the Pythagorean Theorem and Its Applications

The video tutorial reviews various problems solved using the Pythagorean Theorem. It starts with an introduction to the theorem and its proof, followed by examples of calculating areas of squares and finding missing side lengths. The tutorial also covers the converse of the theorem to verify right triangles, calculates the perimeter of a triangle, and finds shortcut distances. Finally, it demonstrates how to calculate the distance between two points using a right triangle.

What formula is used to prove the Pythagorean theorem?

• a^3 + b^3 = c^3

• 2a + 2b = c

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

How do you find the area of square C using the Pythagorean theorem?

• Add a^2 and b^2

• Subtract b^2 from a^2

• Divide c^2 by 2

• Multiply a and b

When finding a missing side length, what is the final step?

• Divide by 2

• Square c

• Take the square root of c^2

• Add a^2 and b^2

What is the area of square B if a = 7 and c^2 = 200?

• 151 inches squared

• 140 inches squared

• 200 inches squared

• 49 inches squared

What is the correct step to find a missing leg in a right triangle?

• Subtract the square of one leg from the hypotenuse

• Add the squares of the two legs

• Divide the hypotenuse by 2

• Multiply the two given sides

How do you determine if a triangle is a right triangle using side lengths?

• a/b = c

• a^2 - b^2 = c^2

• a + b + c = 180

• a^2 + b^2 = c^2

What is the perimeter of a triangle with sides 11, 4.5, and 11.9 cm?

• 27.4 cm

• 26.5 cm

• 25.4 cm

• 24.5 cm

If the side lengths are 60, 80, and 100, does it form a right triangle?

• Only if it's an isosceles triangle

• Yes

• No

• Insufficient information

How much shorter was Robert's shortcut compared to the original path?

• 0.5 miles

• 0.8 miles

• 1 mile

• 1.2 miles

What is the distance between points A and B if the legs of the triangle are 3 and 4 units?

• 5 units

• 7 units

• 8 units

• 6 units