ABCD is a trapezium with AB parallel to CD LM is the line joining midpoints of AD and BC respectively - Maths - Quadrilaterals

Question

ABCD is a trapezium with AB parallel to CD LM is the line
joining midpoints of AD and BC respectively It is given that LM
parallel to AB Prove that LM=1/2(AB+DC)

Lalit Mehra · Accepted Answer

Dear Student!

Join AC and let P be the point of intersection of AC and LM In Î”ADC, L is the mid point of AD and LP||DC (Given) âˆ´ P is the mid point of AC (Converse of Mid Point Theorem) We know that, line joining the midpoint of any two sides of triangle is parallel to the third side and half of it $∴ L P = \frac{1}{2} DC (1)$ In Î”ABC, M and P are the mid points of side BC and AC respectively, $∴ PM = \frac{1}{2} AB (2)$ Adding (1) and (2), we get $L P + PM = \frac{1}{2} AB + \frac{1}{2} DC$ $\Rightarrow L M = \frac{1}{2} (AB + DC)$ Cheers!

ABCD is a trapezium with AB parallel to CD.LM is the line joining midpoints of AD and BC respectively.It is given that LM parallel to AB.Prove that LM=1/2(AB+DC)