Question

In figL || m and m is the mid point of Line segment AB , show that m is also the mid point of CD having it's end points C andD on l and m

Answer 1

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given: m is the mid point of AB
L ll M
to prove :
m is midpoint of CD
proof:
in triangle MCA and triangle MDB
angle AMC = angle BMD( Vertically opp angles)
angle A = angle B(alternate interior angles)
AM=MB (given)
therefore , triangle MCA congruent to triangle MDB by ASA
hence, CM=MD (CPCT)
proved....