Practice Test

Question 8 • Geometry

Which statement proves that PQRS is a parallelogram?

Answer

The midpoint of line segment RP is open paren 4 comma 5 and 1 half close paren and the slope of line segment RP is negative 9 halves .

The midpoint of line segment SQ is open paren 4 comma 5 and 1 half close paren and SQ is equal to 5 .

The slopes of line segment RS and line segment QP are both 3 and SP is equal to RQ is equal to square root of 45 .

The slopes of line segment SP and line segment RQ are both negative 2 and SP is equal to RQ is equal to square root of 45 .

Explanation

In a quadrilateral, if one pair of opposite sides is both parallel and equal in length, the quadrilateral is a parallelogram. In choice A, SP and RQ are opposite sides; their equal slopes of −2 show they are parallel, and both have length √45. Thus, choice A proves that PQRS is a parallelogram.

AI-written and checked against the verified answer.

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