1.  In the given figure ABCD is a square.  M is the midpoint of AB and CM PQ.   Prove that CP = CQ.

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In △PAM and △QBM
∠PAM=∠QBM (90degree each)
AM=MB (As M is the Midpoint of AB)
∠AMP =∠QMP (VOA)
=> △PAM and △QBM (ASA rule)
=>PM=QM (CPCT)
In △CPM and △QBM
CM=CM (common)
∠CMP = ∠CMQ (90degree each)
PM=QM (PROVED Above)
△CPM and △QBM (SAS)
=> CP=CQ (CPCT)

here is answer
 
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