Question

if pq || bc and pr || cd then prove that ar/ ad = aq / ab​

Answer 1

Answer:

In △ABC, we have

PQ∣∣BC

Therefore, by basic proportionality theorem, we have

AB

AQ

=

AC

AP

........(i)

In △ACD, we have

PR∣∣CD

Therefore, by basic proportionality theorem, we have

AC

AP

=

AD

AR

From (i) and (ii), we obtain that

AB

AQ

=

AD

AR

or

AD

AR

=

AB

AQ

[Hence proved]

⇒

AQ

AB

=

AR

AD

⇒

AQ

AQ+QB

=

AR

AR+RD

⇒ 1+

AQ

QB

=1+

AR

RD

⇒

AQ

QB

=

AR

DR

[Hence proved