Question

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

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

Answer 1

The correct option is C If in a triangle $ABC,\angle B\ne \angle C$, then $AB\ne AC$.

Take $p:AB=AC$

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

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

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

$\sim q:\angle B\ne \angle C$

and $\sim p:AB\ne AC$

Thus $\sim q\to \sim p$ is given by

If in a $△ABC,\angle B\ne \angle C$ then $AB\ne AC$.