Question

Fill in the blanks to complete the converse of each property

Answer 1

In general, given the condition p->q,

`\begin{gathered} condition:p\Rightarrow q \\ converse:q\Rightarrow p \end{gathered}`

Therefore, in our case,

1)

`\begin{gathered} p:a\text{ quadrilateral is a trapezoid} \\ q:\text{ it \lparen a quadrilateral\rparen has exactly one pair of parallel sides} \\ Thus, \\ q\Rightarrow p:If\text{ a \lparen quadrilateral\rparen has exactly one pair of parallel sides; then, it is a trapezoid} \end{gathered}`

The answer to the first gap is 'exactly one pair of parallel sides'.

2) Similarly, setting

`\begin{gathered} p:\text{ a trapezoid is isosceles} \\ q:\text{ a trapezoid has congruent legs} \end{gathered}`

Then, the answer to the second gap is 'congruent legs'