Question

3. In the adjoining figure, AB perpendicular BC, AD perpendicular
to CD and BC =CD. Prove that AC bisects angle BAD​

Answer 1

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In the given figure, AB=BC and AC=CD. Prove that: ∠BAD:∠ADB=3:1.

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Solution

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Let ∠ADB=x

In △ACD,AC=CD

⇒∠CAD=∠CDA=x

and, ∠ACB=∠CAD+∠CDA=x+x=2x

⇒∠BAC=∠ACB=2x.(∵ In ABC,AB=BC)

∴∠BAD=∠BAC+∠CAD

=2x+x=3x

And,

∠ADB

∠BAD

=

x

3x

=

1

3

i.e., ∠BAD:∠ADB=3:1 [henceproved]

Answer 2

Step-by-step explanation:

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