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The uploaded document focuses on using the Pythagorean theorem to determine the nature of triangles and to calculate lengths in a right triangle.

Here is a summary:

### Key Concepts:
1. **Property 1: Determining if a Triangle is a Right Triangle**
   - A triangle is right if the square of the longest side equals the sum of the squares of the two other sides.
   - \( c^2 = a^2 + b^2 \) (Pythagorean Theorem).
   - Example calculations confirm whether a triangle is right-angled.

2. **Rappel de Calcul** (Calculation Reminder):
   - To find the square of a number, calculate \( x \times x \).
   - To find a square root, use the \( \sqrt{x} \) function.

3. **Property 2: Calculating a Side Length**
   - In a right triangle, to find a missing side length:
     - Hypotenuse: \( c = \sqrt{a^2 + b^2} \)
     - Leg: \( a = \sqrt{c^2 - b^2} \)

Would you like a detailed solution or explanation for a specific part of this? Let me know if you have a particular problem in mind!

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Here are 5 further exploration questions for better understanding:
1. Can you verify the nature of other triangles using the Pythagorean Theorem?
2. How do you find the hypotenuse in different triangles?
3. What happens if \( c^2 < a^2 + b^2 \)? Is it still a right triangle?
4. Can you generalize these methods to 3D geometry?
5. How do we apply these calculations in real-world problems?

**Tip:** Always re-check which side is the longest before applying the Pythagorean Theorem!

Determine if a triangle is a right triangle given the lengths of its three sides, and calculate missing side lengths in a right triangle using the Pythagorean theorem.

Learn how to determine if a triangle is right-angled by applying the Pythagorean theorem. Explore step-by-step examples to verify triangle types and calculate unknown side lengths in right triangles, suitable for students in Grade 8-9.

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