Question

In the below 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 1

Given that CD is bisected at O by AB
To prove: ar (ΔABC) = ar (ΔABD)
Construction: Draw CP ⊥ AB and DQ ⊥ AB

Proof:-
 `ar  (ΔABC) = 1/2 xx AB xx CP`        ........ (1)

 `ar  (ΔABC) = 1/2 xx AB xx DQ `        ........ (2)

In ∠CPO and ΔDQO

 ∠CPQ = ΔDQO          [Each 90°]

Given that CO = DO

∠COP =  ∠DOQ                                 [vertically opposite angles are equal]     

Than, ΔCPO ≅ DQO                          [By AAS condition]

∴ CP = DQ               ........... (3)            [CP.C.T]

Compare equation (1), (2) and (3)

Area ( ΔABC)a = area of  ΔABD