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Basic Proportionality Theorem

Basic Proportionality Theorem. Mathematics 3 Ochigue , Christle Mae. 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.

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Basic Proportionality Theorem

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  1. Basic Proportionality Theorem Mathematics 3 Ochigue, Christle Mae

  2. 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.

  3. Figure 5.4 shows triangle PQR with line lparalled 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

  4. 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.

  5. References: • http://www.pinkmonkey.com/studyguides/subjects/geometry/chap5/g0505401.asp • Geometry: Applications in Real Life, Pearson

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