Mathematics 3
Ochigue, Christle Mae
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
Consider D PTS and D QTS
Areas of triangles with same height
are in the ratio of their bases.
Similarly
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.
Thus the line l which is parallel to
seg.QR divides seg.PQ and seg.PR
in the same ratio.
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Geometry: Applications in Real Life, Pearson