prove that lf a line parallel to a sideof a triangle interseets remaining side in two distinct points than line dirides the side in the same proportion .
Answers
Basic Proportionality Theorem Proof
Consider a triangle ΔABC, as shown in the given figure. In this triangle, we draw a line PQ parallel to the side BC of ΔABC and intersecting the sides AB and AC in P and Q, respectively.
....................PIC OF TRIANGLE....................
According to the basic proportionality theorem as stated above, we need to prove:
AP/PB = AQ/QC
PROOF IN PIC 2
Conclusion
If P and Q are the mid-points of AB and AC, then PQ || BC. We can state this mathematically as follows:
If P and Q are points on AB and AC such that AP = PB = 1/2 (AB) and AQ = QC = 1/2 (AC), then PQ || BC.
Also, the converse of mid-point theorem is also true which states that the line drawn through the mid-point of a side of a triangle which is parallel to another side, bisects the third side of the triangle.
Hence, the basic proportionality theorem is proved.
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