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.
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
Join S to R and Q to T
PTS and D QTS
Areas of triangles with same height are in the ratio of their bases.
But A ( DQTS
) = A ( D SRT ) as they have a
common base seg.ST and their heights are same as they are between
Thus the line l
which is parallel to seg.QR divides seg.PQ and seg.PR in the same