Question

a line segment joining the midpoints of a parallel sides ab and ac respectively of a Trapezium ABCD is a perpendicular to both the sides Ab and DC . prove that is AD= BC please solve in notebook

Answer 1

consider the diagram

DX=CX, XY is common and angle DXY =angle CXY=90 degree

so by SAS triangle DXY is congruent to triangle CXY

therefore DY = CY and ANGLE 1 = ANGLE 3

ALSO,angle 1 = angle 2 (alternate angles)

angle 3 = angle 4(alternate angles)

angle 2 = angle 4

also AY=BY

therefore by SAS

triangle ADY is congruent to triangle BCY

and so, AD = BC

proved....