Question
upstudy study bank question image url

Match each statement to the correct option provided. In a right- angled triangle, the square of the hypotenuse side equals the sum of the squares theose... Euclidean Theorem sides. \( \quad \begin{array}{l}\text { The Converse of Pythagorean theorem } \\ \text { Pythagorean Theorem }\end{array} \)

Ask by Evans Garrett. in the United States
Jan 24,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

- **Pythagorean Theorem**: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other sides. - **The Converse of Pythagorean theorem**: If the square of one side equals the sum of the squares of the other two sides, then the triangle is right-angled.

Solution

The statement "In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other sides" refers to the Pythagorean Theorem. Thus, the correct match is: - **Pythagorean Theorem**: In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other sides. The other option, "The Converse of Pythagorean theorem," is a different statement that asserts if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. So, the final matching is: - **Pythagorean Theorem**: In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other sides. - **The Converse of Pythagorean theorem**: If the square of one side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

The Deep Dive

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Picture a right triangle where the sides measure 3 units and 4 units; you'll find that the hypotenuse will measure 5 units, which is derived from the equation \( 3^2 + 4^2 = 5^2 \). Now, as for the Converse of the Pythagorean theorem, it goes the other way around! If you have a triangle where the square of one side equals the sum of the squares of the other two, then you've got yourself a right triangle. It's like a secret handshake for triangles! If you pick any three lengths and they fit this condition, you can be sure to whip out the protractor and declare it a right angle. How fun is that?

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy