Which of the following triangles is isosceles right angled triangle?

Options

A.
B.
C.
D.

Answer

To determine which triangle is an isosceles right-angled triangle, we need to understand the properties of such triangles.

### Step-by-Step Solution:

1. **Understand the Definition**:
- An isosceles triangle has at least two sides that are equal in length.
- A right-angled triangle has one angle that measures 90 degrees.

2. **Identify the Characteristics**:
- For a triangle to be an isosceles right-angled triangle, it must have:
- Two sides of equal length.
- One angle that is exactly 90 degrees.

3. **Examine the Options**:
- Look at the given triangles and check their angles and side lengths.
- You need to find a triangle that has:
- One angle measuring 90 degrees.
- The two sides that form this right angle must be equal in length.

4. **Analyze Each Triangle**:
- For each triangle option:
- Check if there is a right angle (90 degrees).
- Check if the two sides that form the right angle are of equal length.

5. **Identify the Correct Triangle**:
- After analyzing all the options, the triangle that meets both criteria (one right angle and two equal sides) is the isosceles right-angled triangle.

6. **Conclusion**:
- Based on the analysis, you can conclude which triangle is an isosceles right-angled triangle.