Applying the Pythagorean Theorem: Finding Missing Lengths

In this video, Mr. Backer demonstrates how to use the Pythagorean theorem to find missing lengths in right triangles, specifically focusing on calculating the area of isosceles triangles. The video covers two examples, each involving the calculation of the triangle's height using the Pythagorean theorem, followed by the area calculation using the base and height. Additionally, the concept of Pythagorean triples is introduced, providing a shortcut for identifying side lengths in right triangles without performing full calculations.

What theorem is used to find missing lengths in right triangles?

• Pythagorean theorem

• Thales' theorem

• Euclid's theorem

• Fermat's Last Theorem

What is the height of the first triangle discussed?

• 14 units

• 13 units

• 12 units

• 10 units

How is the area of a triangle calculated?

• Base plus height

• Base times height

• 1/2 times base times height

• Base times height divided by 2

What is the area of the first triangle?

• 75 units squared

• 70 units squared

• 65 units squared

• 60 units squared

What is the height of the second triangle discussed?

• 22 inches

• 23 inches

• 24 inches

• 25 inches

What is the area of the second triangle?

• 240 inches squared

• 230 inches squared

• 250 inches squared

• 260 inches squared

What defines a Pythagorean triple?

• A set of three whole numbers satisfying a^2 + b^2 = c^2

• A set of three numbers satisfying a + b = c

• A set of three prime numbers

• A set of three even numbers

Which of the following is a Pythagorean triple?

• 2, 3, 4

• 6, 8, 9

• 5, 7, 8

• 3, 4, 5

If a triangle has sides 30 and 50, what is the length of the missing side?

• 40

• 50

• 30

• 20

How can Pythagorean triples help in finding triangle sides?

• By calculating the perimeter

• By defining the types of triangles

• By offering a shortcut to avoid complex calculations

• By providing a formula for the area