Answered

Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.

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}

Sagot :

GinnyAnsweridn
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.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.