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Mathematics

In △ABC, AB = BC, AD ⊥ BC and CE ⊥ AB. Prove that AD = CE.

Triangles

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Answer

In △ABC, AB = BC, AD ⊥ BC and CE ⊥ AB. Prove that AD = CE. Chapterwise Revision (Stage 1), Concise Mathematics Solutions ICSE Class 9.

Given: In △ABC, AB = BC, AD ⊥ BC and CE ⊥ AB.

To prove: AD = CE

Proof: In △ ABD and △ CBE,

AB = BC (Given)

∠ADB = ∠CEB (Both are 90°)

∠ABD = ∠CBE (Common angle)

By ASA congruency criterion,

△ ABD ≅ △ CBE

By corresponding parts of congruent triangles

Hence, AD = CE.

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