Question

C is the midpoint of line segment AB P and Q are midpoint of the segment AC and BC respectively Probe that AP=BQ=one fourth of AB

Answer 1

as C is the mid point of AB...
so it divides AB in two equal halves..
which gives AC=BC -----(i)
as P is the mid point of AC..
AP=CP ------(ii)
As Q is the mid point of BC
CQ=QB -----(iii)
From eq(i) we get
AC=BC
AP+PC=CQ+BQ [from eq(ii) and (iii)]
AP+AP=BQ+BQ
2AP=2BQ
AP=BQ [Hence proved]

AP+PC+CQ+BQ=AB. [AP=PC & CQ=BQ]
AP+AP+BQ+BQ=AB
2AP+2BQ=AB. [AP=BQ]
2AP+2AP=AB
4AP=AB
AP=1/4AB. [Hence proved]