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Ted Mielczarek · Answer 1 · 2020-02-14T18:17:30+0000

Answer:

$\bullet\quad\overline{QR}\cong\overline{ST}\text{ and }\overline{QR}\parallel\overline{ST}\\\\\bullet\quad\overline{QR}\cong\overline{ST}\text{ and }\overline{QT}\cong\overline{RS}$

Explanation:

A quadrilateral is a parallelogram when opposite sides are parallel. This will be the case when ...

one pair of opposite sides are parallel and the same length (choice B)
each pair of opposite sides is the same length (choice E)

An isosceles trapezoid has one pair of parallel sides and the other pair of opposite sides the same length, so that is not sufficient to describe a parallelogram. (Choices A and C describe this condition.)

A line segment is always congruent to itself, so that fact establishes nothing about a parallelogram. (choice D)

_____

Comment on opposite sides equal

Choice E can also describe an hourglass-shaped figure. We assume here that the quadrilateral is convex, with no sides crossing each other.

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