SOLUTION: Prove that ((AC)^2/(BC)^2)=(AD/BD) In right triangle ACB (C is the right angle) with CD as an altitude (D is between A and B)

Algebra ->  Algebra  -> Triangles -> SOLUTION: Prove that ((AC)^2/(BC)^2)=(AD/BD) In right triangle ACB (C is the right angle) with CD as an altitude (D is between A and B)      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 64166: Prove that ((AC)^2/(BC)^2)=(AD/BD) In right triangle ACB (C is the right angle) with CD as an altitude (D is between A and B)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that ((AC)^2/(BC)^2)=(AD/BD) In right triangle ACB (C is the right angle) with CD as an altitude (D is between A and B)
TRIANGLES ADC AND ACB ARE SIMILAR SINCE
ANGLE CAD = ANGLE CAB........SAME ANGLE AREM EXTENDED
ANGLE ADC =90 = ANGLE ACB..GIVEN
HENCE
AD/AC = AC/AB
AC^2=AD*AB..............1
SIMILARLY TRIANGLES BCD AND BAC ARE SIMILAR SINCE
ANGLE CBD=ANGLE CBA
ANGLE BDC = 90 = ANGLE BCA ...HENCE
BC/BA = BD/BC
BC^2=BA*BD.................2
EQN.1/EQN.2...GIVES
AC^2/BC^2 = AD*AB/AB*BD=AD/BD...PROVED