Question
In the given figure, if $\text{AB}=\text{AC}$ and $\angle\text{B}=\angle\text{C}.$ Prove that $\text{PQ}=\text{CP}.$ 
✓
Answer
It is given that $\text{AB}=\text{AC},$ and $\angle\text{B}=\angle\text{C}$
We have to prove that $\text{BQ}=\text{CP}$
We basically will prove $\triangle\text{ABQ}\cong\triangle\text{ACP}$ to
show $\text{BQ}=\text{CP}$ In $\triangle\text{ABQ}$ and $\triangle\text{ACP}$
$\angle\text{B}=\angle\text{C}$ (Given) $\text{AB}=\text{AC}$
(Given) And $\angle\text{A}$ is common in both the triangles
So all the properties of congruence are satisfied
So $\triangle\text{ABQ}\cong\triangle\text{ACP}$
Hence $\text{BQ}=\text{CP}$ Proved.
We have to prove that $\text{BQ}=\text{CP}$
We basically will prove $\triangle\text{ABQ}\cong\triangle\text{ACP}$ to
show $\text{BQ}=\text{CP}$ In $\triangle\text{ABQ}$ and $\triangle\text{ACP}$
$\angle\text{B}=\angle\text{C}$ (Given) $\text{AB}=\text{AC}$
(Given) And $\angle\text{A}$ is common in both the triangles
So all the properties of congruence are satisfied
So $\triangle\text{ABQ}\cong\triangle\text{ACP}$
Hence $\text{BQ}=\text{CP}$ Proved.
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