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 is expressed as a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If a right triangle has legs of length 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

What are Pythagorean Triples?

Back

Pythagorean Triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, meaning a² + b² = c².

Front

Are the numbers 8, 15, and 17 a Pythagorean Triple?

Back

Yes, because 8² + 15² = 64 + 225 = 289 = 17².

Front

What is the length of the missing side if one leg is 6 and the hypotenuse is 10?

Back

Using the Pythagorean Theorem: c² = a² + b²; 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8.

Front

If a = 5 and b = 12, what is c?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

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

Back

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

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.