Determining if a Triangle is a Right Triangle Using the Pythagorean Theorem

Regarding side length, a triangle is a right triangle if …

A triangle is a right triangle if and only if it satisfies the Pythagorean theorem

A triangle is a right triangle if and only if it satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let’s label the sides of a triangle as follows:

– Side a: The side adjacent to angle A
– Side b: The side adjacent to angle B
– Side c: The hypotenuse, opposite the right angle (angle C)

In a right triangle, the Pythagorean theorem can be written as:

c^2 = a^2 + b^2

So, if you know the lengths of any two sides of a triangle, you can determine if it is a right triangle by checking if the square of the longest side’s length is equal to the sum of the squares of the other two sides’ lengths.

For example, let’s say you have a triangle with side lengths of 3 cm, 4 cm, and 5 cm. To determine if it is a right triangle, you can apply the Pythagorean theorem:

c^2 = a^2 + b^2
5^2 = 3^2 + 4^2
25 = 9 + 16
25 = 25

Since the equation is true, we can conclude that the triangle with side lengths of 3 cm, 4 cm, and 5 cm is a right triangle.

However, if the equation doesn’t hold true, then the triangle is not a right triangle. For example, if we have a triangle with side lengths of 3 cm, 4 cm, and 6 cm:

c^2 = a^2 + b^2
6^2 = 3^2 + 4^2
36 = 9 + 16
36 ≠ 25

In this case, the equation is not true, so the triangle with side lengths of 3 cm, 4 cm, and 6 cm is not a right triangle.

More Answers: