Pythagorean Review 2

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). Formula: a² + b² = c².

Front

What is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c². Example: (3, 4, 5) is a Pythagorean Triple.

Front

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

Back

To find the length of the hypotenuse (c), use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

What is the distance formula in coordinate geometry?

Back

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

Front

Does the set of numbers 10, 24, 26 represent a Pythagorean Triple?

Back

Yes, because 10² + 24² = 100 + 576 = 676 = 26².

Front

How can you determine if 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.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

If one side of a right triangle is 9 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(9² + 12²) = √(81 + 144) = √225 = 15.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.