Q.8. In the adjacent figure, AM is a median, M P ∥ C A a n d P R ∥ B C . Prove that (i) AB = 2AP (ii) AM = 2AR (iii) BM = 2PR (iv) BC = 4PR. Share with your friends Share 4 Abhishek Jha answered this Dear Student, Here is the solution of your asked query: (i) MP∥CA and AM is median This means M is the midpoint of BC.So by Midpoint theorem we have;P is the midpoint of AB.So we haveBP=AP⇒BP+AP=AP+AP⇒AB=2AP(ii) In △ABMPR∥BC and P is the midpoint of ABSo by midpoint theorem we have;R is the midpoint of AMso, AM=2AR(iii) Since P and R are the midpoints of AB and AM respectively and PR//BCSo, PR=12BM⇒BM=2PR(iv) BC=2BM {Since M is the median}⇒BC=2×2PR=4PR Regards 4 View Full Answer Kabir answered this in triangle ABC (i) PM || AC M is midpoint of BC (AM is median) by converse midpoint theorem P is the midpoint of AB therefore, AP=BP AP+BP=AB AP+AP=AB AB=2AP (ii) similarly, in triangle ABM R is midpint of AM 1
