Math, asked by sdesalesinv, 5 months ago

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 AlastorMadEyeMoody
1

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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