# Which of the triangles are right triangles?

A triangle having an angle of 90^{°} is called a right-angled triangle.

## Answer: By the use of the Pythagoras property, we conclude that only option 2 is the right-angled triangle.

Let's determine the right-angled triangle from the options.

**Explanation:**

We need to make use of the Pythagoras property for the right-angled triangle.

We know that the Pythagoras theorem is satisfied only in right triangles. Pythagora property states, (Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}

Since the Pythagoras theorem holds true only in the right-angled triangle, so we can verify the above options, by putting them one by one in the Pythagoras theorem.

Option 1) (3)^{2} + (5)^{2} = 34 ≠ 35. Thus, it is not a right-angled triangle.

Option 2) (5)^{2} + (4)2 = 41 = 41. Thus, it is a right-angled triangle.

Option 3) (6)^{2} + (8)^{2} = 100 ≠ 10. Thus, it is not a right-angled triangle.

Option 4) (3)^{2} + (3)^{2} = 18 ≠ 27. Thus, it is not a right-angled triangle.

### Hence, by the use of the Pythagoras property, we conclude that only option 2 is the right-angled triangle.

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