Question

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

Answer 1

Figure is in the attachment.

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.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

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.

HOPE THIS ANSWER WILL HELP YOU…~

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