<span>In logic, the converse of a conditional statement is the result of reversing its two parts. For example, the statement P → Q, has the converse of Q → P.
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the converse is 'if a figure is a parallelogram, then it is rectangle.' As can be seen, the converse statement is not true, hence the truth value of the converse statement is false. </span> The inverse of a conditional statement is the result of negating both the hypothesis and conclusion of the conditional statement. For example, the inverse of P <span>→ Q is ~P </span><span>→ ~Q. </span><span><span>For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the inverse is 'if a figure is not a rectangle, then it is not a parallelogram.' As can be seen, the inverse statement is not true, hence the truth value of the inverse statement is false.</span> </span> The contrapositive of a conditional statement is switching the hypothesis and conclusion of the conditional statement and negating both. For example, the contrapositive of <span>P → Q is ~Q → ~P. </span> <span><span>For the given statement, 'If a figure is a rectangle, then
it is a parallelogram.' the contrapositive is 'if a figure is not a parallelogram,
then it is not a rectangle.' As can be seen, the contrapositive statement is true, hence the truth value of the contrapositive statement is true.</span> </span>
Based on the Angle Bisector theorem, the opposite sides of ∆ABC are divided into proportional segments alongside the two other sides of the triangle, as BD bisects the <ABC. This implies that:
