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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

What is the square root of 25?

Back

The square root of 25 is 5.

Front

In the equation a² + b² = c², what do a and b represent?

Back

In the equation, a and b represent the lengths of the two legs of a right triangle.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is derived from the Pythagorean Theorem and is used to find the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 6² + 8² = c²; 36 + 64 = c²; 100 = c²; c = 10.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

True or False: You add a² and c² to find b in a right triangle.

Back

False. You add a² and b² to find c (the hypotenuse).

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.