Question

can it be concluded that the given parallelogram is either a rhombus, a rectangle, or a square? explain.
a. the parallelogram is a rhombus.
b. from the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.
c. the parallelogram is a rectangle.
d. the parallelogram is a square.
explain the reason for the determination made in the previous step.
a. the diagonals of the parallelogram are congruent.
b. the diagonal of the parallelogram bisects a pair of opposite angles.
c. the diagonals of the parallelogram are perpendicular.
d. from the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.
e. the parallelogram is both a rhombus and a rectangle.

Explanation:

A parallelogram is a rhombus if a diagonal bisects a pair of opposite angles. The diagram shows a diagonal creating congruent angles at opposite vertices, meaning it bisects those angles. A rectangle requires congruent diagonals, and a square needs both rhombus and rectangle properties, which aren’t indicated here.

Answer:

A. The parallelogram is a rhombus.
B. The diagonal of the parallelogram bisects a pair of opposite angles.