Mathematics
AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.
Triangles
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Answer
Let CD intersect AB at point O.
In △ AOD and △ BOC,
⇒ ∠DAO = ∠CBO (Both equal to 90°)
⇒ ∠DOA = ∠COB (Vertically opposite angles are equal)
⇒ AD = BC (Given)
∴ ∆ AOD ≅ ∆ BOC (By A.A.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ AO = OB.
Hence, proved that CD bisects AB.
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