Topic
Given quadrilateral ABCD. Consider the proposition “If quadrilateral ABCD is a rectangle, then quadrilateral ABCD has two equal diagonals”. The inverse of that proposition is:
A. “If quadrilateral ABCD is a rectangle, then quadrilateral ABCD has no two equal diagonals”
B. “If quadrilateral ABCD does not have two equal diagonals, then quadrilateral ABCD is not a rectangle”
C. “If quadrilateral ABCD has two equal diagonals, then quadrilateral ABCD is not a rectangle”
D. “If quadrilateral ABCD has two equal diagonals, then quadrilateral ABCD is a rectangle”
Solution method – See details
The inverse of the clause \(P \Rightarrow Q\) (or “If P then Q”) is \(Q \Rightarrow P\) “If Q then P”
Detailed explanation
P: “quadrilateral ABCD is a rectangle”
Q: “quadrilateral ABCD has two equal diagonals”
The converse of the proposition \(P \Rightarrow Q\) is: “If quadrilateral ABCD has two equal diagonals, then quadrilateral ABCD is a rectangle”.
Choose D.
