Given: the coordinates of triangle pqr are p(0, 0), q(2a, 0), and r(2b, 2c). prove: the line containing the midpoints of two sides of a triangle is parallel to the third side. as part of the proof, find the midpoint of line pq.

Given: Coordinates of ΔPQR are P( 0 , 0 ) , Q( 2a , 0 ) and  R( 2b , 2c )

To Proof: Line containing the midpoints x & Y of two sides PQ & PR of a triangle is parallel to the third side QR .i.e XY║QR

First We find Mid Point of side PQ and PR say X & Y respectively and then we find slope of line XY and QR. As if there slope is equal then they are parallel.

Formula of Mid point is given by

So, Coordinated of Mid Point of PQ , X =

                                                          =

                                                          = ( a , 0 )

Coordinates of Mid Point of PR, Y =

                                                         =

                                                         = ( b , c )

Slope of a line is given by,

Slope of Line XY =

                            =

Slope of Line QR =

                            =

                            =

Since, Slope of XY = Slope of QR

⇒ XY is parallel to QR

Hence proved

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