In the PQ ll side BC and seg QR || side AB.
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Asked on December 20, 2019 by
Althaf Bogimi
in the figure,
seg PQ∥side BC and
seg QR∥side AB.
i) Find
QC
AQ
.
ii) What would be
RB
CR
? Hence find
RC
BR
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ANSWER
In ΔAPQ & ΔABC
∠BAC=∠PAQ (same angle)
∠ABC=∠APQ (PQ∥BC)
∠AQP=∠ACB (PQ∥BC)
Triangles are similar
AQ
AC
=
AP
AB
=
3
5
AQ
AC
−1=
AQ
AC−AQ
=
3
5
−1=
3
2
⇒
AQ
QC
=
3
2
,
QC
AQ
=
2
3
(ii) ΔCQR and ΔCAB
∠ACB=∠QCR (same angle)
∠CQR=∠CAB (QR∥AB)
∠CRQ=∠CBA (QR∥AB)
Triangles are similar
CR
RB
+1=
CR
RB+CR
=
CR
CB
CR
CB
=
CQ
CA
=
2
5
CR
CB
=
2
5
CR
RB
=
2
5
−1
CR
RB
=
2
3
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