Question

The converse of "If in a triangle $ABC,AB=AC$, then $\angle B=\angle C$", is

• A. lf in a triangle $ABC,\angle B=\angle C$, then $AB=AC$.
• B. lf in a triangle$ABC,AB\ne AC$, then $\angle B\ne \angle C$.
• C. lf in a triangle $ABC,\angle B\ne \angle C$, then $AB\ne AC$.
• D. lf in a triangle $ABC,\angle B\ne \angle C$, then $AB=AC$ .

Answer 1

The correct option is A lf in a triangle $ABC,\angle B=\angle C$, then $AB=AC$.

Take $p:AB=AC$

and $q:\angle B=\angle C$

So the given statement is symbolically represented as $p\to q$

Now by definition, Converse of a conditional statement $p\to q$ is $q\to p$

So $q\to p$ is given by

"If in a triangle $ABC,\angle B=\angle C,$ then $AB=AC.$"