Question

3. In Figure 6, AB=AD and angle BAC= angle DAC.
Prove that line segment CA bisects angle BCD
Fig. 6​

Answer 1

Answer:

In Triangle ABC and Triangle ADC

AB= AD (Given)

∠BAC=∠DAC (Given)

AC=AC (Common)

Hence, Triangle ABC is congruent to Triangle ADC by SAS congruence rule.

Therefore ∠ACB=∠ACD by CPCT. So we know that AC bisects ∠C.

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Answer 2

Answer:

line segment AC bisects angle C

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