Question

3. PQRS is a parallelogram. L and M are points
on PQ and SR respectively such that
PL = MR. Show that LM and OS bisect each
other​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given

PQRS is a parallelogram .l and m are points on pq and sr respectively such that pl=mr.

to proof

show that lm and qs bisect each other.

proof

let we name the point at which the line lm and qs intersect be O

so, In triangle LOQ and MOS

PL = MR(given)

QP=SR

QP-PL=SR-MR

QL=SM

<SOM=<QOL(vertically opp angles)

<OSM=<OQL(alternate angles)

triangle LOQ ≅triangle MOS(by AAS rule of congruency)

∴ SO=QO and LO=MO (by c.p.c.t)

Hence,LM and QS bisect each other