Exploring the Pythagorean Theorem

This video provides a quick overview of right triangles and the Pythagorean theorem. It explains the properties of right triangles, including the hypotenuse and legs, and demonstrates how to use the Pythagorean theorem to find missing side lengths. The video includes examples with both integer and non-integer solutions, emphasizing the importance of exact answers. It also covers scenarios where the hypotenuse is given, and a leg needs to be found, highlighting the correct setup of the equation.

What is the name of the longest side in a right triangle?

• Base

• Angle

• Hypotenuse

• Leg

Which sides of a right triangle are called legs?

• The two sides opposite the acute angles

• The two sides forming the right angle

• The two longer sides

• The two shorter sides

In the Pythagorean theorem, what does the equation a^2 + b^2 = c^2 represent?

• Relationship between the sides of a right triangle

• Perimeter of the triangle

• Sum of angles

• Area of the triangle

If one leg of a right triangle is 3 and the other is 4, what is the length of the hypotenuse?

• 12

• 5

• 7

• 6

What is a Pythagorean triple?

• A set of three angles in a triangle

• A set of three prime numbers

• A set of three side lengths that satisfy the Pythagorean theorem

• A set of three integers that are all odd

If the legs of a triangle are 8 and 12, what is the approximate length of the hypotenuse?

• 14.42

• 20

• 16

• 10

How do you find a missing leg in a right triangle if the hypotenuse and one leg are known?

• Add the squares of the hypotenuse and the known leg

• Subtract the square of the known leg from the square of the hypotenuse

• Divide the hypotenuse by the known leg

• Multiply the known leg by the hypotenuse

What is the approximate value of a leg if the hypotenuse is 20 and the other leg is 9?

• 15

• 19

• 17.86

• 18.36

Why is it important to keep exact values in Pythagorean theorem calculations?

• To ensure measurement accuracy

• To avoid using decimals

• To simplify the calculations

• To make it easier to remember

What should the maximum value of a leg be if the hypotenuse is 20?

• Exactly 10

• More than 20

• Exactly 20

• Less than 20