Q. 8

If two diagonals of a quadrilateral ABCD intersect each other perpendicularly, then let us prove that, AB2 + CD2 = BC2 + DA2

Answer :

Given: AC BD



To prove: AB2 + CD2 = BC2 + DA2


Proof:


By applying Pythagoras theorem in ΔAOB, we get,


AB2 = AO2 + BO2 ……………… (1)


By applying Pythagoras theorem in ΔBOC, we get,


BC2 = BO2 + CO2 ……………… (2)


By applying Pythagoras theorem in ΔCOD, we get,


CD2 = CO2 + DO2 ……………… (3)


By applying Pythagoras theorem in ΔDOA, we get,


DA2 = AO2 + DO2 ……………… (4)


By adding eqn. (1) and (3), we get,


AB2 + CD2 = AO2 + BO2 + CO2 + DO2


AB2 + CD2 = (BO2 + CO2) + (AO2 + DO2)


Substituting from eqn. (2) and (4) gives,


AB2 + CD2 = BC2 + DA2


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Pythagoras TheoremQuiz | Pythagoras TheoremQuiz | Pythagoras Theorem48 mins
A Peep into Pythagoras TheoremA Peep into Pythagoras TheoremA Peep into Pythagoras Theorem43 mins
A Peep into Pythagoras TheoremA Peep into Pythagoras TheoremA Peep into Pythagoras Theorem43 mins
History of Pythagoras and His TheoremHistory of Pythagoras and His TheoremHistory of Pythagoras and His Theorem37 mins
Basics of Binomial TheoremBasics of Binomial TheoremBasics of Binomial Theorem39 mins
Foundation | Sum of the SeriesFoundation | Sum of the SeriesFoundation | Sum of the Series43 mins
Basic Proportionality TheoremBasic Proportionality TheoremBasic Proportionality Theorem44 mins
NCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of Arithmetic45 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Basic Proportionality TheoremBasic Proportionality TheoremBasic Proportionality Theorem42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :