Question

select all the correct answers.
if a figure is a square, its diagonals divide it into isosceles triangles.
p: a figure is a square.
q: a figures diagonals divide into isosceles triangles.
which represents the converse of this statement? is the converse true?
□ ( q
ightarrow p )
□ ( sim p
ightarrow sim q )
□ the converse of the statement is false.
□ ( q leftrightarrow p )
□ ( p
ightarrow q )
□ the converse of the statement is sometimes true and sometimes false.
□ the converse of the statement is true

Explanation:

Step1: Recall the definition of converse

The converse of a statement \(p
ightarrow q\) is \(q
ightarrow p\). The original statement is “If a figure is a square (\(p\)), its diagonals divide it into isosceles triangles (\(q\))” (\(p
ightarrow q\)). So its converse is \(q
ightarrow p\).

Step2: Check the truth - value of the converse

Consider a rectangle (which is not a square). The diagonals of a rectangle are equal in length. In a rectangle, the diagonals divide the rectangle into four isosceles triangles (since the diagonals of a rectangle are equal and bisect each other). But a rectangle is not a square. So the converse “If a figure's diagonals divide it into isosceles triangles (\(q\)), then the figure is a square (\(p\))” is false.

Answer:

\(q
ightarrow p\), The converse of the statement is false.