Define thales theirem

1.	Define thales theirem
Answer» Basic Proportionality Theorem was first stated by Thales, a Greek mathematician. Hence it is also known as Thales Theorem. Thales first initiated and formulated the Theoretical Study of Geometry to make astronomy a more exact science. What is this theorem that Thales found important for his study of astronomy? Let us find it out.Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.Basic Proportionality TheoremIn the figure alongside, if we consider DE is parallel to BC, then according to the theorem,ADBD=AECELet’s not stop at the statement, we need to find a proof that its true. So shall we begin?PROOF OF BPTGiven: In ΔABC, DE is parallel to BCLine DE intersects sides AB and PQ in points D and E, such that we get triangles A-D-E and A-E-C.To Prove: ADBD=AECEConstruction: Join segments DC and BEProof:In ΔADE and ΔBDE,A(ΔADE)A(ΔBDE)=ADBD (triangles with equal heights)In ΔADE and ΔCDE,A(ΔADE)A(ΔCDE)=AECE (triangles with equal heights)Since ΔBDE and ΔCDE have a common base DE and have the same height we can say that,A(ΔBDE)=A(ΔCDE)Therefore,A(ΔADE)A(ΔBDE)=A(ΔADE)A(ΔCDE)Therefore,ADBD=AECE If a line is drawn parallel to 1 side of a traingle to intersect the other 2 sides in distinct point, then the other 2 sides are divided in the same ratio.

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