Question

plz solve 23. plzzzzzzz​

Answer 1

Given,

In triangle ABC

angle C = 90

AC =BC

D is a point on AB

Now, when a line intersect the hypotenuse from the 90 degree angle then the line intersect to the the hypotenuse is perpendicular and divide it in two equal parts.

In triangle ABC, apply Pythagoras Theorem

AB^2 = AC^2 + BC^2

Because of AC=BC

AB^2 = 2AC^2......................................................(1).'

In triangle ACD , apply Pythagoras Theorem ,

AC^2 = AD^2 + CD^2 ...................(2)

Now substitute equation (2) in (1)

AB^2 = 2[ AD^2 + CD^2 ]

WE know that. AB = AD + CD

(AD + BD ) ^2 = 2AD^2 + 2CD^2

AD^2 + BD^2 + 2ADBD = 2AD^2 + 2CD^2

AD = BD [ By theorem written above]

AD^2 + BD^2 + 2AD^2 = 2AD^2 + 2CD^2

AD^2 + BD^2 = 2CD^2 [Proved]