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Question

If l,m,n are three parallel lines and the transversal t1 and t2 cut the lines l,m,n at the points A,B,C and P,O,R as shown in the figure, then

98622_caf26623b5744f9eaef96a56f625a750.png

A
ABBC=POOR
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B
ABOR=BCPO
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C
APBO=BOCR
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D
ABPO=APBO
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Solution

The correct option is A ABBC=POOR
In triangle ABD and ACE
A is common
D=E=90
ABD=ACE (since m || n)

Thus both the triangle are similar.

Hence, ABBC=ADDE
Similarly, triangle PRT and POS are similar

Hence, POOR=PSST
Since, l||m||n, the perpendicular distance between them will be equal.

Hence, AD=PS and DE=ST

or, ABBC=POOR

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