Question

In tringle ABC , if angle C =90°, then ________is the hypotenuse.​

Answer 1

Answer:

The correct answer is AB.

Step-by-step explanation:

In tringle ABC , if angle C =90°, then AB is the hypotenuse.

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Answer 2

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ACD

AD  

2

=AC  

2

+CD  

2

   .....(1)

In △ACB

A B  

2

−AC  

2

=BC  

2

    .....(2)

As CD=DB=  

2

BC

​  

   ...... (3)

Substituting (3) in (1)

AD  

2

=AC  

2

+  

4

BC

​  

 

2

 

4AD  

2

−4AC  

2

=BC  

2

    ....... (4)

Subtracting (2) from (4)

4AD  

2

−4AC  

2

−( A B  

2

−AC  

2

)=BC  

2

−BC  

2

 

4AD  

2

−4AC  

2

−A B  

2

+AC  

2

=0  

4AD  

2

−3 A C  

2

=A B  

2

 

Hence proved.