In Fig., ABC and ABD are two triangles on the same base AB. If line se

1.	In Fig., ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar.(∆ABC) = ar.(∆ABD).
Answer» Data: ∆ABC and ∆ABD are two triangles on the same base AB. Line segment CD bisected by AB at O’. To Prove: ar.(∆ABC) = ar.(∆ABD) Prove: AB bisects line segment CD at O’. ∴ OC = OD In ∆ADC, AO is the median on CD. ∴ ar.(∆AOD) = ar.(∆AOC) …………… (i) In ∆BDC, BO is the median on CD. ∴ ar.(∆BOD) = ar.(∆BOC) ……………. (ii) Adding (i) and (ii), ar.(∆AOD) + ar.(∆BOD) = ar.(∆AOC)+ ar.(∆BOC) ∴ ar.(∆ABD) = ar.(∆ABC)

In Fig., ABC and ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar.(∆ABC) = ar.(∆ABD).

Answer»

Data: ∆ABC and ∆ABD are two triangles on the same base AB.

Line segment CD bisected by AB at O’.

To Prove: ar.(∆ABC) = ar.(∆ABD)

Prove: AB bisects line segment CD at O’.

∴ OC = OD In ∆ADC, AO is the median on CD.

∴ ar.(∆AOD) = ar.(∆AOC) …………… (i)

In ∆BDC, BO is the median on CD.

∴ ar.(∆BOD) = ar.(∆BOC) ……………. (ii)

Adding (i) and (ii),

ar.(∆AOD) + ar.(∆BOD) = ar.(∆AOC)+ ar.(∆BOC)

∴ ar.(∆ABD) = ar.(∆ABC)