In triangle ABC ,AB=AC,BD PERPENDICULAR AB. …
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Sia ? 5 years, 9 months ago
Given: ΔABC with AB = AC
And AD = CD, AE = BE.
To prove: BD = CE
Proof: In ΔABC we have
AB = AC [Given]
⇒12AB=12AC
⇒ AE = AD
[∵ D is the mid-point of AC and E is the mid-point of AB]
Now, in ΔABD and ΔACE, we have
AB = AC [Given]
∠A=∠A (Common angle]
AE = AD [Proved above]
SO, by SAS criterion of congruence, we have
ΔABD≅ΔACE
⇒ BD = CE [CPCT]
Hence, proved.
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