AD and BC are equal perpendiculars to a line segment AB (see Figure). Show that CD bisects AB.
Solution:
In
and
.
, But these are alternate interior angles. It means that
.
(Alternate Interior Angles,
)
BC=AD (Given)
(Given)
Therefore, by ASA rule, we have
Hence, BO=AO (Corresponding Parts of Congruent Triangles)
It means that CD bisects AB.
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