ADC:
2. In a triangle ABC, right-angled at B, BD is
drawn perpendicular to AC.
Prove that:
(i) ZABD = ZC (ii) ZCBD = ZA
Answers
Answered by
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Step-by-step explanation:
In ∆ABC,
ang. A + ang. B + ang. C = 180° ... (1)
ang. A + 90° + ang. C = 180°
ang. A + ang. C = 90° ... (2)
In ∆ABD,
ang. A + ang. ABD + ang. BDA = 180° ... (3)
Now, Ang. BDA = 90° (PERPENDICULAR DRAWN)
Therefore,
ang. A + 90° + ang. ABD = 180°
ang. A + ang. ABD = 90°... (4)
from (2) and (4),
ang. C = ang. ABD ...(#)
In ∆CDB,
ang. C + ang. CBD + ang. CDB = 180° ... (5)
Now, ang. CDB = 90° (PERPENDICULAR DRAWN)
Therefore,
ang. C + ang. CBD + 90° = 180°
ang. C + ang. CBD = 90°
Now, from (2),
ang. CBD = ang. A ...(#)
Hence, proved.
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