4. Which of the following can be the sides of a right triangle?
(i) , , 6 cm.
(ii) 2 cm, 2 cm, 5 cm.
(iii) , 2cm, .
In the case of right-angled triangles, identify the right angles.
As we know,
In a Right-angled Triangle: By Pythagoras Theorem,
(i) , , 6 cm.
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 6.5 cm
Verifying the Pythagoras theorem,
Hence it is a right-angled triangle.
The Right-angle lies on the opposite of the longest side (hypotenuse) So the right angle is at the place where 2.5 cm side and 6 cm side meet.
(ii) 2 cm, 2 cm, 5 cm.
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 5 cm
Verifying the Pythagoras theorem,
Hence it is Not a right-angled triangle.
(iii) , 2cm, .
As we know the hypotenuse is the longest side of the triangle, So
Hypotenuse = 2.5 cm
Verifying the Pythagoras theorem,
Hence it is a Right-angled triangle.
The right angle is the point where the base and perpendicular meet.