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 the hypotenuse in a right triangle?

Back

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

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

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

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

What is the formula to find the distance between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs (the shorter sides) of a right triangle.

Front

If a right triangle has legs of length 6 and 8, what is the length of the hypotenuse?

Back

The hypotenuse is 10 (using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

Front

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

Back

The relationship is defined by the Pythagorean Theorem: a² + b² = c².

Front

Is the statement 'the side opposite the right angle is the shortest side' true or false?

Back

False. The side opposite the right angle (the hypotenuse) is the longest side.

Front

If a right triangle has a hypotenuse of 15 and one leg of 9, what is the length of the other leg?

Back

The other leg is 12 (using the Pythagorean Theorem: 9² + b² = 15², so 81 + b² = 225, thus b² = 144, and b = 12).