Q7 of 49 Page 21

□ ABCD is a parallelogram point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE.

In Δ CED and ΔBET

⇒ ∠ CED≅ ∠ BET (opposite angles)


⇒ ∠ CDE≅ ∠ BTE (Alternate angles)


(∵ AB||DC ⇒ BT||DC, as BT is extension to AB)


⇒ Δ CED ~ Δ BET (By AA Test)


⇒ (corresponding sides are proportional)


⇒ DE× BE = CE×TE


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