Question

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

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Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a figure
• AB $\perp$ BC and AD $\perp$ CD
• BC = CD

To Prove:

• We have to prove that AC bisects ∠BAD
• Simply ∠ BAC = ∠ DAC

Solution:

In ∆ABC and ∆ADC

• BC = DC [ Given ]
• AC = AC [ Common side ]
• ∠ABC = ∠ADC [ Each 90 ° ]

Hence By R.H.S rule

$\implies$ ∆ABC $\cong$ ∆ADC

Therefore

$\implies$ ∠ BAC = ∠ DAC [ By CPCT ]

Hence AC Bisects ∠ BAD

Answer 2

Step-by-step explanation:

Answer is in the attachment