9. AABC and ADBC lie on the same side of BC,
as shown in the figure. From a point P on
BC, PQ | AB and PR || BD are drawn, meeting
AC at Q and CD at R respectively. Prove that
OR AD
Answers
Answered by
6
Hey mate here is your answer....
Step-by-step explanation:
Given Two triangles ABC and DBC lie on the same side of the base BC. Points P,Q and R are points on BC,AC and CD respectively such that PR||BD and PQ||AB.
To prove QR||AD
Proof In △ABC, we have
PQ∣∣AB
∴
PB
CP
=
QA
CQ
........(i) [By Basic proportionality Theorem]
In △BCD, we have
PR∣∣BD
∴
PB
CP
=
RD
CR
........(ii) [By Thale's Theorem]
From (i) and (ii), we have
QA
CQ
=
RD
CR
Thus, in △ACD, Q and R are points on AC and CD respectively such that
QA
CQ
=
RD
CR
⇒ QR∣∣AD [By the converse of Basic Proportionality Theorem]
Hope it helps you....
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