Pythagorean Theorem Basics

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: c² = a² + b².

Front

In a right triangle, which side is always the longest?

Back

The hypotenuse is always the longest side in a right triangle.

Front

If one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 cm.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

The formula is derived from the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

If the hypotenuse of a right triangle is 13 cm and one leg is 5 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² = c² - b². Here, a² = 13² - 5² = 169 - 25 = 144, so a = √144 = 12 cm.

Front

What is a right triangle?

Back

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

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.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25).

Front

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

Back

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