Pythagorean Theorem Review

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: c² = a² + b².

Front

What is a right triangle?

Back

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

Front

How do you identify the hypotenuse in a right triangle?

Back

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

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the distance formula in coordinate geometry?

Back

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

Front

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

Back

27 feet (Using the Pythagorean Theorem: 10² + 25² = 100 + 625 = 725; √725 ≈ 26.9, rounded to 27 feet).

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem: c² = a² + b².

Front

If the sides of a triangle are 9, 40, and 41, is it a right triangle?

Back

Yes, it is a right triangle (41² = 9² + 40²).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

How can you determine if a triangle with sides 2.1, 7.2, and 7.5 is a right triangle?

Back

Yes, it is a right triangle (7.5² = 2.1² + 7.2²).