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). This can be expressed as a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What does the letter 'c' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse, which is the side opposite the right angle.

Front

What do the letters 'a' and 'b' represent in the Pythagorean Theorem?

Back

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

Front

How can you determine if a set of three numbers can form a right triangle?

Back

To determine if three numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers. If a² + b² = c² holds true, then they can form a right triangle.

Front

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

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: a² + b² = c².

Front

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

Back

No, the Pythagorean Theorem specifically applies to right triangles only.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

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

Back

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