Q8 of 45 Page 43

In figure 3.51, in ΔABC, seg AD and seg BE are altitudes and AE = BD.

Prove that seg AD ≅ seg BE


Given: AD and BE are altitudes


AE = BD


To prove: AD ≅ BE


Proof: AD and BE are altitudes


∠ADB = ∠BEA = 90° [Given]


In ΔADB and ΔBEA


BD = AE [Given]


∠ADB = ∠BEA = 90° [Given]


AB = BA [Common side of both the triangles]


∴ By RHS congruency


ΔADB ≅ ΔBEA


So, AD ≅ BE [corresponding sides of congruent triangles]


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