ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Figure). Show that:
(i)
(ii) AP = CQ
Solution (i)
In
and
, we have
(Alternate Interior angles,
)
(Each given equal to
)
AB=CD (Opposite sides of parallelogram are equal)
Therefore, by AAS congruence rule,
Solution (ii)
We have showed in solution (i) that
(Corresponding parts of congruent triangles are equal)
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