Mathematics
In the given figure, median AD of △ABC is produced. If BL and CM are perpendiculars drawn on AD and AD produced, prove that BL = CM.
Triangles
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Answer
In △ABC,
AD is the median on side BC
⇒ BD = DC
In △LDB and △CDM,
⇒ BD = DC [Given, AD is the median]
⇒ ∠L = ∠M [Each equal to 90°]
⇒ ∠LDB = ∠CDM [Vertically opposite angles are equal]
∴ △LDB ≅ △CDM (By A.A.S. axiom)
⇒ BL = CM [Corresponding part of congruent triangles are equal.]
Hence, proved that BL = CM.
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