AC=AE, AB= AD and angle BAD =angle EAC, Show that BC =DE
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Answer:
what is the figure and what is the polygon
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Solution:
It is given in the question that AB = AD, AC = AE, and ∠BAD = ∠EAC
To prove:
The line segment BC and DE are similar i.e. BC = DE
Proof:
We know that BAD = EAC
Now, by adding DAC on both sides we get,
BAD + DAC = EAC +DAC
This implies, BAC = EAD
Now, ΔABC and ΔADE are similar by SAS congruency since:
(i) AC = AE (As given in the question)
(ii) BAC = EAD
(iii) AB = AD (It is also given in the question)
∴ Triangles ABC and ADE are similar i.e. ΔABC ΔADE.
Hence,
By the rule of CPCT, it can be said that BC = DE.
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