Intro 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 the hypotenuse in a right triangle?

Back

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

Front

What is the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

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

Back

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

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

What does it mean to square a number?

Back

To square a number means to multiply the number by itself. For example, 4 squared (4²) is 4 x 4 = 16.

Front

In the Pythagorean Theorem, what do the letters a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the legs of the right triangle, while 'c' represents the length of the hypotenuse.

Front

What is the area of a square with a side length of 5?

Back

The area of a square is calculated as side length squared. So, area = 5² = 25.

Front

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

Back

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

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.