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 a triangle ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that : AD = CE. Triangles, Concise Mathematics Solutions ICSE Class 9.

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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