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). Formula: a² + b² = c².

Front

What is the formula for finding the distance between two points in a coordinate plane?

Back

The distance formula is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

If one side of a right triangle is 6 units and the other side is 8 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

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

What does 'perimeter' mean in geometry?

Back

Perimeter is the total distance around a two-dimensional shape, calculated by adding the lengths of all its sides.

Front

How do you calculate the perimeter of a rectangle?

Back

Perimeter of a rectangle = 2(length + width).

Front

What is the height of a cone?

Back

The height of a cone is the perpendicular distance from the base to the apex (tip) of the cone.

Front

What is a right triangle?

Back

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

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².