Flashcardizz Quest 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 a right triangle?

Back

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

Front

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

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

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

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: if the rectangle has a width (a) and a length (b), the diagonal (d) can be found using d = √(a² + b²).

Front

What are the side lengths of a 5-12-13 triangle?

Back

The side lengths are 5, 12, and 13, which satisfy the Pythagorean Theorem (5² + 12² = 13²).

Front

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

Back

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

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

27 feet (using the Pythagorean Theorem: 10² + 25² = c², so c = √(100 + 625) = √725 ≈ 27).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

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

Back

Check if the lengths satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.