Question

given a, b, and c as vertices, construct a parallelogram abcd. which of the following describes how to construct a parallelogram abcd? a. draw an arc of radius ab with the pointer at c. draw an arc of radius ab with the pointer on a. let the intersection of the two arcs be point d. draw line - segments ad and cd using a straightedge. b. construct a line parallel to ab and construct a line perpendicular to ab. let the intersection of the two lines be point d. draw line - segments ad and cd using a straightedge. c. draw an arc of radius ab with the pointer at c. draw an arc of radius bc with the pointer at a. let the intersection of the two arcs be point d. draw line - segments ad and cd using a straightedge. d. construct a line parallel to bc and construct a line perpendicular to bc. let the intersection of the two lines be point d. draw line - segments ad and cd using a straightedge.

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram ABCD, AB = CD and BC = AD.

Step2: Analyze option C

If we draw an arc of radius AB with the pointer at C and an arc of radius BC with the pointer at A, the intersection point D will ensure that AB = CD and BC = AD. Then by drawing line - segments AD and CD using a straight - edge, we can construct the parallelogram.

Step3: Analyze option A

Drawing arcs of radius AB from both A and C does not guarantee the correct side - length relationships for a parallelogram.

Step4: Analyze option B

Constructing a line parallel and a line perpendicular to AB does not guarantee the correct side - length relationships for a parallelogram.

Step5: Analyze option D

Constructing a line parallel and a line perpendicular to BC does not guarantee the correct side - length relationships for a parallelogram.

Answer:

C. Draw an arc of radius AB with the pointer at C. Draw an arc of radius BC with the pointer at A. Let the intersection of the two arcs be point D. Draw line segments AD and CD using a straightedge.