Mathematics
In a triangle ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that : AD = CE.
Triangles
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Answer
△ ABC is shown below:
In △ ABD and △ CBE,
⇒ ∠B = ∠B (Common angle)
⇒ ∠ADB = ∠CEB (Both equal to 90°)
⇒ AB = BC (Given)
∴ △ ABD ≅ △ CBE (By A.A.S. axiom).
We know that,
Corresponding parts of congruent triangles are equal.
∴ AD = CE
Hence, proved that AD = CE.
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