https://file.aiquickdraw.com/mathbot/file/1727315655377vvgdonf2.jpg

In the image, the triangle is shown with side lengths \(7\), \(7\), and \(7\sqrt{2}\).

### Step 1: Classifying as Equilateral, Isosceles, or Scalene
- **Equilateral Triangle**: All sides are equal.
- **Isosceles Triangle**: Two sides are equal.
- **Scalene Triangle**: No sides are equal.

Since two sides are equal (\(7\) and \(7\)) and one is different (\(7\sqrt{2}\)), the triangle is **Isosceles**.

### Step 2: Classifying as Right, Obtuse, or Acute
- **Right Triangle**: One angle is exactly \(90^\circ\).
- **Obtuse Triangle**: One angle is greater than \(90^\circ\).
- **Acute Triangle**: All angles are less than \(90^\circ\).

Using the Pythagorean theorem to check if it's a right triangle:
\[
\text{If } a^2 + b^2 = c^2 \text{ (where } c \text{ is the hypotenuse), then the triangle is right.}
\]
Here:
\[
a = 7, \quad b = 7, \quad c = 7\sqrt{2}.
\]
Check:
\[
a^2 + b^2 = 7^2 + 7^2 = 49 + 49 = 98, \quad c^2 = (7\sqrt{2})^2 = 98.
\]
Since \( a^2 + b^2 = c^2 \), the triangle is a **Right Triangle**.

### Conclusion:
- The triangle is **Isosceles**.
- The triangle is **Right**.

Would you like more details or have any questions?

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Here are 5 related questions for practice:
1. How do you classify a triangle when all sides are different?
2. What are the properties of an acute triangle?
3. Can a scalene triangle be a right triangle?
4. How does the Pythagorean theorem help in classifying triangles?
5. What is the sum of angles in any triangle?

**Tip**: The Pythagorean theorem is essential for determining if a triangle is a right triangle when you know the side lengths!

Classify the triangle as equilateral, isosceles, or scalene. Then, classify the triangle as right, obtuse, or acute. The triangle has side lengths of 7, 7, and 7√2.

This problem demonstrates how to classify a triangle with side lengths 7, 7, and 7√2 as isosceles and a right triangle using the Pythagorean theorem. Learn step-by-step how to verify right triangles and understand triangle classification. Suitable for students in Grades 6-8.

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