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°">°°           (Given)
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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