Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
what is proof of converse of basic propornality theorem
Converse of Basic Proportionality TheoremStatement If a line divides any two sides of a triangle (Δ) in the same ratio, then the line must be parallel (||) to the third side.DiagramGiven In ΔABC, D and E are the two points of AB and AC respectively, such that, AD/DB = AE/EC.To Prove DE || BCProof In ΔABC,given, AD/DB = AE/EC ----- (1) Let us assume that in ΔABC, the point F is an intersect on the side AC. So we can apply the Thales Theorem, AD/DB = AF/FC ----- (2) Simplify, in (1) and (2) ==> AE/EC = AF/FC Add 1 on both sides, ==> (AE/EC) + 1 = (AF/FC) + 1 ==> (AE+EC)/EC = (AF+FC)/FC ==> AC/EC = AC/FC ==> EC = FC From the above, we can say that the points E and F coincide on AC. i.e., DF coincides with DE. Since DF is parallel to BC, DE is also parallel BC Hence the Converse of Basic Proportionality therorem is proved
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -