Question

Point P is the mid -point of MN and C is mid point of MP. Prove that, using Euclids axiom, MC =1/2PN

Answer 1

Given:-Point P is the mid -point of MN and C is mid point of MP.

To prove:-MC =1/2PN

Proof:- As P is the mid -point of MN then P divides MN into two equal halves

such that MP=1/2MN=PN ....................(1).(by Euclid's axiom "things which are equal to the same thing are also equal to one another")

Similarly as C is the mid point of MP then MC=1/2MP=CP ................(2)

Now replacing MP by PN from (1)in (2),we get

MC=1/2(PN)...................hence proved.