Question

identify quadrilaterals (level 2)
you only have 6 questions left to raise your score.
question
choose all answers that describe the quadrilateral tuvw if \\(\overline{tu}\parallel\overline{vw}\\), \\(\overline{uv}\parallel\overline{wt}\\), and diagonals are congruent: \\(\overline{tv}\cong\overline{uw}\\).
answer
attempt 1 out of 2
parallelogram
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Recall parallelogram definition

A quadrilateral with both pairs of opposite - sides parallel is a parallelogram. Since $\overline{TU}\parallel\overline{VW}$ and $\overline{UV}\parallel\overline{WT}$, $TUVW$ is a parallelogram.

Step2: Recall rectangle property

In a parallelogram, if the diagonals are congruent, then it is a rectangle. Given $\overline{TV}\cong\overline{UW}$, since $TUVW$ is a parallelogram, it is also a rectangle.

Step3: Analyze other shapes

A rhombus has all - sides equal (not given here), a square has all - sides equal and diagonals congruent (all - sides equality not given), and a trapezoid has only one pair of parallel sides (this has two pairs).

Answer:

A. Parallelogram
B. Rectangle