Pythagorean Theorem

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle, commonly referred to as sides a and b.

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

State the Pythagorean Theorem formula.

Back

The Pythagorean Theorem states that a² + b² = c², where c is the length of the hypotenuse.

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 = 36 + 64 = 100, so c = √100 = 10.

Front

What does the Pythagorean Theorem help us find?

Back

The Pythagorean Theorem helps us find the length of a side in a right triangle when the lengths of the other two sides are known.

Front

Is the statement 'a² + b³ = c⁴' true or false?

Back

False. The correct formula is a² + b² = c².

Front

If the hypotenuse is 13 and one leg is 5, how do you find the other leg?

Back

Use the formula: a² + 5² = 13². So, a² + 25 = 169, thus a² = 144, and a = √144 = 12.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the lengths of the legs (a and b) equals the square of the length of the hypotenuse (c).

Front

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

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which equals 5².