Question

Two side of AB and BC and median AM of triangle ABC are respectively equal to sides PQ and QR and median PN of triangle POR ...Show that triangleABM =~ triangle PQN

Answer 1

AB/PQ=BC/QR=AM/PN (GIVEN)

THEREFORE

AB/PQ=1/2BM/1/2QN=AM/PN

AB/PQ=BM/QN=AM/PN

AR(TRIANGLE ABM)/AR(TRIANGLEPQN)=AB/PQ=BM/QN=AM/PN=1

THEREFORE

(AB/PQ)^2=1^2

AB=PQ .....1

(AM/PN )^2=1^2

AM=PN .....2

(BM/QN)^2=1^2

BM=QN ...3

CONSIDER A TRAINGLE ABM AND TRAINGLE PQN

AB=PQ FROM 1

BM=QN FROM3

AM=PN FROM2

THEREFORE TRAINGLE ABM CONGRUENT TO TRAINGLE PQN

HENCE PROVRD