Pythagorean Review 20 questions

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

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

Back

To find the length of the hypotenuse, use the Pythagorean theorem: c = √(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 (a and b) and the hypotenuse (c).

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 satisfy the Pythagorean theorem: 3² + 4² = 5².

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Front

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

Back

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

Front

What is the significance of the diagonal in a rectangle?

Back

The diagonal of a rectangle can be calculated using the Pythagorean theorem, as it forms a right triangle with the length and width.

Front

If one side of a right triangle is 5 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the converse of the Pythagorean theorem?

Back

The converse states that if a triangle has side lengths a, b, and c such that a² + b² = c², then the triangle is a right triangle.