lo figure, ABCD is a parallelogram in which
PQ parallel to BC and AB parallel to QR. Find the length of AP?
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Given : ABCD is a parallelogram
PQ || BC
AB || QR
To Find : length of AP
Solution:
ABCD is a parallelogram
=> AB || CD and AB = CD
BC || AD and BC = AD
Thale's theorem BPT
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
PQ || BC
in ΔABC
AQ/QC = AP /PB
=> AQ/QC = AP /3
Similarly in ΔADC
AB || QR
=> QR || CD
Hence AQ/QC = AR/DR
=> AQ/QC = 10/2
=> AQ/QC = 5
AQ/QC = AP /3
=> 5 = AP/3
=> AP = 15
length of AP = 15 cm
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