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

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse (c) in a right triangle, you can use the Pythagorean Theorem: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

What is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c). The hypotenuse is the longest side and is opposite the right angle.

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

A triangle with sides of lengths 5, 12, and 13 is a right triangle, as it satisfies the Pythagorean Theorem: 5² + 12² = 13².

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths (a² + b² = c²).

Front

What is the formula for calculating the distance traveled in a right triangle scenario?

Back

The distance traveled can be calculated using the Pythagorean Theorem if the path forms a right triangle. The total distance is the sum of the lengths of the two legs.

Front

What is the significance of the square root in the Pythagorean Theorem?

Back

The square root is used to find the length of the hypotenuse when the lengths of the other two sides are known, as it allows you to solve for c in the equation a² + b² = c².

Front

What is the height of a cone in relation to the Pythagorean Theorem?

Back

The height of a cone can be found using the Pythagorean Theorem if the radius and slant height are known, as they form a right triangle with the height.

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.