Questions: In the quadrilateral BLUE shown, overline BE is congruent to overline UL. Which information would be sufficient to prove that quadrilateral BLUE is a parallelogram. - overline LU is congruent to overline EU - overline LU is congruent to overline BE - overline BE is congruent to overline BL - overline BL is congruent to overline EU

In the quadrilateral BLUE shown, overline BE is congruent to overline UL. Which information would be sufficient to prove that quadrilateral BLUE is a parallelogram.
- overline LU is congruent to overline EU
- overline LU is congruent to overline BE
- overline BE is congruent to overline BL
- overline BL is congruent to overline EU

Transcript text: In the quadrilateral BLUE shown, $\overline{B E} \cong \overline{U L}$. Which information would be sufficient to prove that quadrilateral BLUE is a parallelogram. $\overline{L U} \cong \overline{E U}$ $\overline{L U} \cong \overline{B E}$ $\overline{B E} \cong \overline{B L}$ \[ \overline{B L} \cong \overline{E U} \]

Solution

Solution Steps

Step 1: Analyze the given information

We are given that $\overline{BE} \cong \overline{UL}$ . We are looking for which additional information would be sufficient to prove that BLUE is a parallelogram.

Step 2: Consider the options

If $\overline{LU} \cong \overline{EU}$ , this would make triangle LUE an isosceles triangle, but this information doesn't tell us anything about the rest of the quadrilateral, nor does it relate to the given information.
If $\overline{LU} \cong \overline{BE}$ , together with $\overline{BE} \cong \overline{UL}$ , we have one pair of opposite sides congruent and parallel. This is a condition that proves a quadrilateral is a parallelogram.
If $\overline{BE} \cong \overline{BL}$ , this tells us that triangle BEL is isosceles, but this information doesn't help us prove BLUE is a parallelogram.
If $\overline{BL} \cong \overline{EU}$ , together with the given information $\overline{BE} \cong \overline{UL}$ , we have two pairs of opposite sides congruent. This condition is enough to prove BLUE is a parallelogram.