In Figure. AB = AD and = . then i. ......... . ii. BC =................. iii. =.......... iv. Line segment AC bisects .......... and ..........

In and , AB = AD [given] AC = AC [common side] = [given] By SAS congruence criterion, Now, BC = DC [by CPCT] Also, = [by CPCT] Line segment AC bisects and . Since, = and =

In Figure. AB = AD and = . then i. ......... . ii. BC =..........…

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Question

In Figure. $AB = AD$ and $\angle\text{BAC}=\angle\text{DAC}.$ then
$i. \triangle.........\cong\triangle\text{ABC}.$
$ii. \text{BC} =.................$
$iii. \angle\text{BCA}=..........$
$iv.$ Line segment $AC$ bisects $..........$ and $..........$

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Answer

In $\triangle\text{ABC}$ and $\triangle\text{ADC},$
$\text{AB} = \text{AD} [$given$]$
$AC = AC [$common side$]$
$\angle\text{BAC}=\angle\text{DAC} [$given$]$
By $\ce{SAS}$ congruence criterion,
$\triangle\text{ADC}\cong\triangle\text{ABC}$
Now,$\text{ BC} =\text{ DC} [$by $\ce{CPCT}]$
Also, $\angle\text{BCA}=\angle\text{DCA} [$by $\ce{CPCT}]$
Line segment $AC$ bisects $\angle\text{BAD}$ and $\angle\text{BCD}.$
Since, $\angle\text{BAC}=\angle\text{DAC}$
and $\angle\text{BCA}=\angle\text{DCA}$