5.4 Basic Proportionality Theorem
If a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.
![](Image154.gif)
Figure 5.4
Figure 5.4 shows triangle PQR with line l
paralled to seg.QR. l
intersects seg.PQ and seg.PR at S and T respectively.
To prove that ![](Image155.gif)
Join S to R and Q to T
Consider D
PTS and D QTS
![](Image156.gif)
Areas of triangles with same height are in the ratio of their bases.
Similarly ![](Image157.gif)
But A ( DQTS
) = A ( D SRT ) as they have a
common base seg.ST and their heights are same as they are between
parallel lines.
![](Image158.gif)
Thus the line l
which is parallel to seg.QR divides seg.PQ and seg.PR in the same
ratio.
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