In `A B C` and `P Q R` Figure, `A B=P Q ,B C=Q R` and `C B` and `R Q` are extended to `X` and `Y` respectively and `/_A B X` =`/_P Q Ydot` Prove that `A B C~=P Q Rdot` Figure

Explanation

In `ΔABC` and `ΔPQR`
`AB=PQ` and `BC=QR`
`CB` and `RQ` extended to `X` and `Y`.
`∠ABX=∠PQY`
`∠ABC=180^@−angleABX=180^@=∠PQY`
`∠PQR=180 ^@−∠PQY=∠ABC`
We get in both triangles,
`AB=PQ`
`BC=QR`
`∠ABC=∠PQR`
Then both triangle are congruent, i.e. `ΔABCcongΔPQR`.