If the sum of squares of two sides is equal to square of third side then `DeltaABC` is

Options

A. Equilateral
B. Isosceless
C. Scalene
D. Right angled

Answer

To solve the problem, we need to analyze the given condition regarding the sides of triangle ABC.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
Let the sides of triangle ABC be denoted as \( A \), \( B \), and \( C \).

2. **Understand the given condition**:
We are given that the sum of the squares of two sides is equal to the square of the third side. This can be mathematically expressed as:
\[ A^2 + B^2 = C^2 \]

3. **Recall the Pythagorean theorem**:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

4. **Apply the Pythagorean theorem**:
According to the theorem, if \( A^2 + B^2 = C^2 \), then \( C \) must be the hypotenuse, and the triangle ABC must be a right triangle with the right angle opposite to side \( C \).

5. **Conclude the type of triangle**:
Since we have established that \( A^2 + B^2 = C^2 \), we conclude that triangle ABC is a right triangle with angle \( C \) being \( 90^\circ \).

### Final Answer:
Triangle ABC is a right triangle.

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