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For each of the following quadrilaterals, select all the properties that must be true.

\begin{tabular}{|l|c|c|c|c|}
\hline & Four right angles & Only one pair of parallel sides & Two pairs of parallel sides & All sides congruent \\
\hline (a) Trapezoid & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline (b) Square & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline (c) Parallelogram & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Sure, let's examine the properties that must be true for each type of quadrilateral listed.

### (a) Trapezoid

1. Four right angles: No, a trapezoid does not necessarily have four right angles.
2. Only one pair of parallel sides: Yes, by definition, a trapezoid has exactly one pair of parallel sides.
3. Two pairs of parallel sides: No, a trapezoid does not have two pairs of parallel sides.
4. All sides congruent: No, a trapezoid does not necessarily have all sides congruent.

So, the selection for a trapezoid is:
- Four right angles: ☐
- Only one pair of parallel sides: ☑
- Two pairs of parallel sides: ☐
- All sides congruent: ☐

### (b) Square

1. Four right angles: Yes, a square has four right angles.
2. Only one pair of parallel sides: No, a square has two pairs of parallel sides.
3. Two pairs of parallel sides: Yes, a square has two pairs of parallel sides.
4. All sides congruent: Yes, all sides of a square are congruent.

So, the selection for a square is:
- Four right angles: ☑
- Only one pair of parallel sides: ☐
- Two pairs of parallel sides: ☑
- All sides congruent: ☑

### (c) Parallelogram

1. Four right angles: No, a parallelogram does not necessarily have four right angles.
2. Only one pair of parallel sides: No, a parallelogram has two pairs of parallel sides.
3. Two pairs of parallel sides: Yes, a parallelogram has two pairs of parallel sides.
4. All sides congruent: No, a parallelogram does not necessarily have all sides congruent.

So, the selection for a parallelogram is:
- Four right angles: ☐
- Only one pair of parallel sides: ☐
- Two pairs of parallel sides: ☑
- All sides congruent: ☐

Here is the completed table based on the analysis:

[tex]\[ \begin{tabular}{|l|c|c|c|c|} \hline & Four right angles & Only one pair of parallel sides & Two pairs of parallel sides & All sides congruent \\ \hline (a) Trapezoid & ☐ & ☑ & ☐ & ☐ \\ \hline (b) Square & ☑ & ☐ & ☑ & ☑ \\ \hline (c) Parallelogram & ☐ & ☐ & ☑ & ☐ \\ \hline \end{tabular} \][/tex]

This table correctly reflects the properties that must be true for each type of quadrilateral.

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