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: c² = a² + b².

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 shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

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

Back

The hypotenuse is 15 feet.

Front

How do you find the length of one leg of a right triangle if you know the hypotenuse and the other leg?

Back

You can use the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the length of the known leg.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

In a right triangle, if one leg is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

The other leg is 12.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem.

Front

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the height of a ladder against a wall or finding the distance across a rectangular field.

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.