Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What is the formula to find the hypotenuse in a right triangle?

Back

The formula to find the hypotenuse (c) is: c = √(a² + b²).

Front

If one side of a right triangle is 15 and the other side is 20, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(15² + 20²) = √(225 + 400) = √625 = 25.

Front

In the equation 15² + x² = 21², what does x represent?

Back

x represents the length of one of the legs of the right triangle.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If the lengths of the two legs of a right triangle are 9 and 12, what is the length of the hypotenuse?

Back

c = √(9² + 12²) = √(81 + 144) = √225 = 15.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

If a² + b² = c² holds true for the lengths of the sides, then the triangle is a right triangle.

Front

What is the value of x in the equation x² + 15² = 21²?

Back

x² + 225 = 441; x² = 441 - 225; x² = 216; x = √216 ≈ 14.7.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).