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 are the sides 'a' and 'b' in a right triangle?

Back

In a right triangle, 'a' and 'b' are referred to as the legs of the triangle, which are the two sides that form the right angle.

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

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: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

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

Back

The sum of the areas of the squares on the legs (a and b) is equal to the area of the square on the hypotenuse (c).

Front

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

Back

Using the Pythagorean Theorem: c² = a² + b²; 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12.

Front

What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

Back

The formula is: a² = c² - b², where 'c' is the hypotenuse and 'b' is the known leg.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

What is the value of the hypotenuse if both legs are equal and each leg measures 4?

Back

Using the Pythagorean Theorem: c² = 4² + 4²; c² = 16 + 16; c² = 32; c = √32 or approximately 5.66.

Front

If a right triangle has legs measuring 9 and 12, what is the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12²; c² = 81 + 144; c² = 225; c = 15.