Question

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

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

Answer 1

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

Take $p:AB>AC$

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

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

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

Thus $q\to p$ is given by

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