In Fig. ABC and ABD are two triangles on the base AB. If line segment

1.	In Fig. ABC and ABD are two triangles on the base AB. If line segment CD is bisected by AB at O, Show that ar(Δ ABC) = ar(Δ ABD).
Answer» Given that, CD bisected AB at O To prove : Area (ΔABC) = Area (ΔABD) Construction : CP perpendicular to AB and DQ perpendicular to AB Proof : Area (ΔABC) = \(\frac{1}{2}\)(AB x CP) ...(i) Area (ΔABD) = \(\frac{1}{2}\)(AB x DQ) ...(ii) In ΔCPO and ΔDQO, We have, ∠CPO = ∠DQO (Each 90°) Given that, CO = DO ∠COP = ∠DOQ (Vertically opposite angle) Then, by AAS congruence rule, ΔCPO ≅ ΔDQO Therefore, CP = DQ (By c.p.c.t) Thus, Area (ΔABC) = Area (ΔABD) Hence, proved

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

Answer»

Given that,

CD bisected AB at O

To prove :

Area (ΔABC) = Area (ΔABD)

Construction :

CP perpendicular to AB and DQ perpendicular to AB

Proof :

Area (ΔABC) = \(\frac{1}{2}\)(AB x CP) ...(i)

Area (ΔABD) = \(\frac{1}{2}\)(AB x DQ) ...(ii)

In ΔCPO and ΔDQO,

We have,

∠CPO = ∠DQO

(Each 90°)

Given that,

CO = DO

∠COP = ∠DOQ

(Vertically opposite angle)

Then,

by AAS congruence rule,

ΔCPO ≅ ΔDQO

Therefore,

CP = DQ

(By c.p.c.t)

Thus,

Area (ΔABC) = Area (ΔABD)

Hence, proved