In △ ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3 : 1.
Mid-point Theorem
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Question

In △ ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3 : 1.

KnowledgeBoat · Accepted Answer

Draw DY || BQ. In △ BCQ and △ DCY, ⇒ ∠BCQ = ∠DCY (Common) ⇒ ∠BQC = ∠DYC (Corresponding angles are equal) ∴ △ BCQ ~ △ DCY (By A.A. axiom) We know that, Corresponding sides of similar triangle are proportional. ..........(1) Since, D is the mid-point of BC. ∴ BC = 2CD Considering L.H.S. of the equation (1), we get : In △ AEQ and △ ADY, ⇒ ∠EAQ = ∠DAY (Common) ⇒ ∠AEQ = ∠ADY (Corresponding angles are equal) ∴ △ AEQ ~ △ ADY (By A.A. axiom) We know that, Corresponding sides of similar triangle are proportional. (Since, E is the mid-point of AD) ............(2) Dividing equation (1) by (2), we get : Hence, proved that BE : EQ = 3 : 1.

Mathematics

In △ ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3 : 1.

Mid-point Theorem

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