5. In the given figure, ABCD is a parallelogram. F anE are the-mid poi

1.	5. In the given figure, ABCD is a parallelogram. F anE are the-mid points of ABand BC respectively.Prove that DB bisects LM.
Answer» Construction: Join pointsAandC and letACandDBintersect atG. LetDBintersectEFatH. Proof: Diagonals of a parallelogram bisect each other. ⇒AG=CG. By the midpoint theorem,EF∥AC. ⇒△EHB∼△AGBand△FHB∼△CGB. ⇒EH/AG=EB/AB andFH/CG=FB/CB. ButEB/AB=1=FB/CBsinceEandFare the midpoints ofABandBCrespectively. ⇒EH/AG=FH/CG⇒EH/FH=AG/CG=1 ⇒EH=FH. ⇒DBbisectsEF. Like my answer if you find it useful! how triangle EHB~ triangle AGB

5. In the given figure, ABCD is a parallelogram. F anE are the-mid points of ABand BC respectively.Prove that DB bisects LM.

Answer»

Construction: Join pointsAandC and letACandDBintersect atG.

LetDBintersectEFatH.

Proof:

Diagonals of a parallelogram bisect each other.

⇒AG=CG.

By the midpoint theorem,EF∥AC.

⇒△EHB∼△AGBand△FHB∼△CGB.

⇒EH/AG=EB/AB andFH/CG=FB/CB.

ButEB/AB=1=FB/CBsinceEandFare the midpoints ofABandBCrespectively.

⇒EH/AG=FH/CG⇒EH/FH=AG/CG=1

⇒EH=FH.

⇒DBbisectsEF.

Like my answer if you find it useful!

how triangle EHB~ triangle AGB