Pythagorean 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: a² + b² = c².

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

The distance can be found using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

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 (the two sides that form the right angle) and the hypotenuse (the side opposite the right angle).

Front

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

Back

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

Front

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

Back

The sides 5, 12, and 13 form a right triangle, satisfying the Pythagorean Theorem: 5² + 12² = 13².

Front

How do 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.

Front

What is the hypotenuse of a right triangle with legs measuring 6 cm and 8 cm?

Back

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

Front

What is the distance from the point (1, 2) to the point (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

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

Back

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