Pyhtagorean 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: c² = a² + b².

Front

What are Pythagorean Triples?

Back

Pythagorean Triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean Theorem. For example, (3, 4, 5) and (5, 12, 13) are Pythagorean Triples.

Front

Is the set of numbers 8, 15, 17 a Pythagorean Triple?

Back

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

Front

What is the first step in using the Pythagorean Theorem to find the length of a side?

Back

Identify the lengths of the two sides of the right triangle that are known (a and b) and determine which side you need to find (c).

Front

If a triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100 = 10².

Front

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

Back

The formula is c = √(a² + b²).

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625 = 25².

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

Can a triangle with sides 5, 12, and 13 be a right triangle?

Back

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

Front

What do you do to solve for c in the equation a² + b² = c²?

Back

Take the square root of both sides after calculating a² + b².