Exploring the Pythagorean Theorem and Right Triangles

This video introduces the Pythagorean theorem, a fundamental concept in mathematics, particularly in geometry and trigonometry. It explains the properties of right triangles, focusing on identifying the hypotenuse. The video demonstrates how to apply the theorem to calculate unknown sides of a triangle through practical examples, including finding both the hypotenuse and a shorter side.

What is a right triangle?

• A triangle with no right angles

• A triangle with all sides equal

• A triangle with one angle measuring 90 degrees

• A triangle with two equal sides

What is the hypotenuse in a right triangle?

• The shortest side of the triangle

• The side opposite to the right angle

• The side adjacent to the right angle

• The side with the least area

What does the Pythagorean theorem apply to?

• Right triangles

• Equilateral triangles

• Any triangle

• Isosceles triangles

According to the Pythagorean theorem, how do you calculate the length of the hypotenuse?

• A + B squared = C

• A squared - B squared = C squared

• A + B = C

• A squared + B squared = C squared

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

• 5

• 7

• 6

• 9

Why do we only consider the positive root when solving for sides of a triangle?

• Because the negative root is used for other calculations

• Because it's a mathematical convention

• To simplify the calculation

• Because side lengths can't be negative

In a right triangle, if the hypotenuse is known, how can you find the length of one of the other sides?

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

• Add the squares of the hypotenuse and the known side

• Divide the hypotenuse by the known side

• Multiply the squares of the hypotenuse and the known side

What is the length of side B if side A is 6 and the hypotenuse is 12 in a right triangle?

• 6

• 108

• 6 square roots of 3

• 12

How do you simplify the square root of 108?

• Square root of 36 times 3

• 18

• Square root of 54

• 6 square roots of 3

What is the formula to find the length of a side other than the hypotenuse in a right triangle?

• A squared + B squared = C

• C squared - A squared = B squared

• A squared + C squared = B

• C squared + A squared = B squared