if PQ||BC and PR||CD then prove that AR/AD=AQ/AB
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Step-by-step explanation:
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]
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