verify weather a triangle with the given side lenght is a right angled triangle 9,10,15

To verify whether a triangle with side lengths 9, 10, and 15 is a right-angled triangle, we can apply the **Pythagorean theorem**. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. 

The Pythagorean theorem is:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the hypotenuse (the longest side),
- \(a\) and \(b\) are the other two sides.

Given:
- \(a = 9\),
- \(b = 10\),
- \(c = 15\) (since it's the longest side).

Now, let's verify if this satisfies the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

\[
15^2 = 9^2 + 10^2
\]

\[
225 = 81 + 100
\]

\[
225 = 181
\]

Since \(225 \neq 181\), the given triangle **is not** a right-angled triangle.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:
1. What is the Pythagorean theorem, and how does it apply to right-angled triangles?
2. Can a triangle be classified by angles if it's not right-angled?
3. How do you identify the hypotenuse in a right-angled triangle?
4. What other methods can verify triangle types based on their sides?
5. How does the converse of the Pythagorean theorem help in identifying right-angled triangles?

**Tip:** Always remember, the longest side of a triangle is the hypotenuse when checking for right-angled triangles!

verify whether a triangle with the given side lengths is a right-angled triangle 9, 10, 15

Learn how to verify if a triangle with side lengths 9, 10, and 15 is a right-angled triangle using the Pythagorean theorem. This solution breaks down key geometric concepts and provides a detailed step-by-step verification. Suitable for students in Grades 8-10.

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