BD and CE are median of ∆ ABC. Prove that:area( ∆GBC)area(AEGD). – InterviewSolution

1.

BD and CE are median of ∆ ABC. Prove that:area( ∆GBC)area(AEGD).

Answer»

(i) Since, BD and CE are medians.

AD = DC

AE = BE

Hence, by converse of Basic Proportionality theorem,

ED || BC

In ΔEGD and ΔCGB,

∠DEG = ∠GCB (alternate angles)

∠EGD = ∠BGC (Vertically opposite angles)

ΔEGD ~ ΔCGB (AA similarity)

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