Question

9. OLMNO is a parallelogram, on the diagonal LN
N
B
take points A and B such that LA = NB.
Prove that sqare OAMB is a parallelogram.​

Answer 1

Answer:

let LM and BAD intersect at O

as AL = CM and AB = CD

therefore AB-AL=CD-CM

BL = DM ___ (i)

consider ∆OMD and ∆OLB

• <DOM = <BOL (vertically opposite angles)

• <OMD = <OLB (alternate interior angles)

• DM = BL (from i)

therefore ∆OMD congruent to ∆OLB

therefore OM = OL, OD = OB (CPCT)

therefore O bisects LM and BD

therefore LM, BD bisect each other