FLASHCARD - 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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

How do you determine if three sides can form a right triangle?

Back

To determine if three sides can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

If one side of a right triangle is 8 cm and the other is 15 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 cm.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

Calculate the length of the hypotenuse if the other two sides are 6 feet and 8 feet.

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 feet.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

If the hypotenuse is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: 13² = 5² + b². Therefore, 169 = 25 + b², so b² = 144, and b = √144 = 12.

Front

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

Back

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

Front

If a right triangle has an area of 24 square units and a base of 8 units, what is the height?

Back

Using the area formula: 24 = (1/2) * 8 * height. Therefore, height = 24 / 4 = 6 units.