In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
Question:
In the given figure, AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
Solution:
Given: In the given figure, AD and BC are equal perpendiculars to a line segment AB.
To prove: CD bisects AB
Proof:
In ΔAOD and ΔBOC,
∠DAO = ∠CBO = 90
AD = BC (Given)
∠DOA = ∠COB (Vertically opposite angles)
∴ By AAS congruence criteria,
ΔAOD ≅ ΔBOC
∴ AO = BO (CPCT)
Hence, CD bisects AB.
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