Q. 4 4.5( 55 Votes )

In Fig. 6.59, ABC is a triangle in which ABC < 90° and AD BC. Prove that

Answer :

To Prove: AC2AB2 + BC2 - 2BC x BD

Given: AD is Perpendicular on BC and angle ABC < 90°


Pythagoras Theorem :  It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Applying Pythagoras theorem in Δ ADB, we obtain

AD2 + DB2 = AB2

AD2 = AB– DB2          .....eq(i)

Applying Pythagoras theorem in Δ ADC, we obtain

AD2 + DC2 = AC2

AB2– BD2 + DC2 = AC2     [Using equation (i)]

AB2– BD2 + (BC - BD)2 = AC2      [ DC = BC - BD]

AC2 = AB2– BD2 + BC2 + BD2 -2BC x BD

AC2 = AB2 + BC2 - 2BC x BD

Hence, Proved.

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