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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)
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Solution
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
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