Final answer:
The figure could be a parallelogram if: One pair of opposite sides measures 10 in, and the other pair measures 13 in (Option 1) and One pair of opposite sides measures 10 in, and the other pair measures 8 in (Option 2).
The answer is option ⇒1 and 2
Explanation:
To determine if the given figure could be a parallelogram, we need to examine the measurements of its sides.
Option 1:
Yes, one pair of opposite sides could measure 10 in, and the other pair could measure 13 in.
In a parallelogram, opposite sides are congruent. Therefore, if one pair of opposite sides measures 10 in, and the other pair measures 13 in, it is possible for the figure to be a parallelogram.
Option 2:
Yes, one pair of opposite sides could measure 10 in, and the other pair could measure 8 in.
In a parallelogram, opposite sides are congruent. Therefore, if one pair of opposite sides measures 10 in, and the other pair measures 8 in, it is possible for the figure to be a parallelogram.
Option 3:
No, there are three different values when each expression is set equal to 10.
In a parallelogram, opposite sides are congruent. However, if there are three different values when each expression is set equal to 10, it means that the opposite sides are not congruent. Therefore, the figure cannot be a parallelogram.
Option 4:
No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
In a parallelogram, opposite sides are congruent. If the value of x that makes one pair of sides congruent does not make the other pair of sides congruent, it means that the opposite sides are not congruent. Therefore, the figure cannot be a parallelogram.
Based on the given options, the figure could be a parallelogram if:
- One pair of opposite sides measures 10 in, and the other pair measures 13 in (Option 1).
- One pair of opposite sides measures 10 in, and the other pair measures 8 in (Option 2).
The answer is option ⇒1 and 2