Solving Lesson 3 Page 7 Math Workbook 10 – Kite>

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.