Question

Prove that:

A line passing through the midpoints of two sides of a triangle is parallel to and half the length of the third side of the triangle.

Answer 1

(11 Let un consider triangle PQR het X and Y bemid point of P Q and PR respectively P Y IM Q construction: Draw RM parallel to PQ Join X Y and ym. To prove XY1QR XY = IQ R Prood LPYX is equal to LRYM LPXY is equal to LRMY ti vertically opposite angle B ARTH E.PQ IRM] PY=YR [:' Y is mid point] So AP Y = ARMY [ASA congruent rute] .: PX= RM and XY = YM t corresponding sides of Leand congruent triangles are equal] R M = 2x = XQ ->

WKT PQ 11 MR From 1 and ② The Quadnilateral XM RQ in parallelogram, itora XQ = MR XQ IIMR i XM II QR L'opp niden ol parellelogram are parallet ] Hence XVIIQR I WKT QR = XM Q R = XY+YM QR = X Y + XY Q R = 2XY XY = I QR [ KÝ : y eo 7 Hence the proof

The proof for the above question can be found in the attached image.Please go through AAS congruent rule before analysing the proof

(Note - the figure is roughly drawn,kindly dont worry about its measurement)