Question

If D and E are points on sides AB and AC respectively of a ΔABC such that DE||BC and BD = CE. Prove that ΔABC is isosceles.

Answer 1

Answer:

SOLUTION :

GIVEN : In Δ ABC, DE || BC and BD = CE.

To prove : Δ ABC is isosceles.

AD / BD = AE/EC

[By using basic proportionality theorem]

AD = AE

[ BD = CE ]

So, AD + BD = AE + CE.

[BD = CE & AD = AE]

Therefore, AB = AC.

Hence, Δ ABC is isosceles.

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Answer 2

Answer:

Step-by-step explanation:

AD / BD = AE/EC

[By using basic proportionality theorem]

AD = AE

[ BD = CE ]

So, AD + BD = AE + CE.

[BD = CE & AD = AE]

Therefore, AB = AC.

Hence, Δ ABC is isosceles.

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