Question

Write the converse of the statement.
In $\vartriangle ABC$, if AB = AC, then C = B.

Answer 1

We will first understand the logistics of the converse statements. We will then consider the statement given in the form “If p then q” and turn it into “If q then p”. Thus, we will have the answer.

Complete step-by-step answer:
Let us first understand the logistics of finding converse, contrapositive and inverse of any conditional statement.
Let the original conditional statement be in the form: “If p, then q”.
Now, if we have such a statement, then its converse is given by “ If q, then p.”
Comparing “If p, then q” to the given statement which is “In $\vartriangle ABC$, if AB = AC, then C = B”.
Here, ‘In $\vartriangle ABC$’ is the prefix and will remain constant, ‘AB = AC’ is p and ‘C = B’ is q.
Now, we need to write it in the form: If q, then p.
$\therefore$ we will get get:
In $\vartriangle ABC$, if C = B, then AB = AC.

$\therefore$ the required statement is “In $\vartriangle ABC$, if C = B, then AB = AC.”

Note: The students must know the difference between converse, contrapositive and inverse of the
statements.
If we have the original conditional statement in the form: “If p, then q”.
The converse of this conditional statement is given by: “If q, then p”.
The contrapositive of this conditional statement is given by: “If not q, then not p”.
The inverse of this conditional statement is given by: “If not p, then not q”.
$\therefore$ the contrapositive and inverse of the given question will be “In $\vartriangle ABC$, if $C \ne B$, then $AB \ne AC$” and “In $\vartriangle ABC$, if $AB \ne AC$, then $C \ne B$” respectively.
Fun Fact:-
Inverse of contrapositive is converse because the inverse of “If not q, then not p” will be “If q, then p” which is converse.