How does this step ensure that the new angle will be congruent to the original angle?

Answer with Step-by-step explanation:

According to the Pythagorean theorem,

Hypotenuse²=Base²+Perpendicular²

a.

Base=3

Perpendicular=2

3²+2²=13

Hypotenuse=√(13)

Hypotenuse²=13

b.

Base=3√2

Perpendicular=2

(3√2)²+2²=18+4

               =22

Hypotenuse=5

Hypotenuse²=25

c.

Base=3√3

Perpendicular=2

(3√3)²+2²=27+4

               =31

Hypotenuse=√(43)

Hypotenuse²=43

Hence, The only case in which Pythagorean theorem is satisfied is:

a

Hence, Triangle in case a is right angled triangle