Question

In the given figure, $$AB=AC, P$$ and $$Q$$ are points on $$BA$$ and $$CA$$ respectively such that $$AP=AQ$$. Prove that
$$\triangle APC\cong \triangle AQB$$

Answer 1

In the given figure $$AB=AC$$
$$P$$ and $$Q$$ are point on $$BA$$ and $$CA$$ produced respectively such that $$AP=AQ$$
Now we have to prove $$\triangle APC \cong \triangle AQB$$

As $$AB=AC$$

$$AQ+AP$$

and $$\angle BAQ=\angle CAP$$ (opposite angle)

Hence $$\triangle APC \cong \triangle AQB$$

By using corresponding parts of congruent triangle concept we have
$$CP=BQ$$
$$\angle ACP =\angle ABQ$$