Question Video: Identifying Right Triangles from Side Lengths | Nagwa Question Video: Identifying Right Triangles from Side Lengths | Nagwa

Question Video: Identifying Right Triangles from Side Lengths Mathematics • Second Year of Preparatory School

Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

In a triangle 𝐴𝐵𝐶, if (𝐴𝐵)² = (𝐵𝐶)² + (𝐴𝐶)², which angle is the right angle?

02:01

Video Transcript

In a triangle 𝐴𝐵𝐶, if 𝐴𝐵 squared is equal to 𝐵𝐶 squared plus 𝐴𝐶 squared, which angle is the right angle?

In this question, we are given an equation involving the sum of the squares of two side lengths in a triangle being equal to the square of the length of the remaining side. And we want to determine which angle is a right angle. We can do this by recalling the Pythagorean theorem.

We can recall that this tells us that in any right triangle 𝑋𝑌𝑍 with a right angle at 𝑍, we have that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two shorter sides. So 𝑋𝑌 squared is equal to 𝑌𝑍 squared plus 𝑋𝑍 squared. An interesting and useful fact about the Pythagorean theorem is that it works in both directions. If we have three side lengths in a triangle that satisfy the equation 𝑋𝑌 squared is equal to 𝑌𝑍 squared plus 𝑋𝑍 squared, then it must be a right triangle with a right angle opposite the hypotenuse.

We are told that 𝐴𝐵 squared is equal to 𝐵𝐶 squared plus 𝐴𝐶 squared. So we must have that these points form a right triangle with right angle opposite the hypotenuse. Since 𝐴𝐵 is the hypotenuse, the right angle must be opposite this side at vertex 𝐶. Hence, the right angle in the triangle is angle 𝐶.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy