100 Points Activity
Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is 45°. How many parallelograms can you construct given these conditions? What are the lengths of the sides and the measurements of the angles for the parallelogram(s)?

Complete the steps below to solve the problem.

Part A
Using a ruler and protractor, draw a parallelogram that satisfies the given conditions. (If you don’t have these tools available, draw it freehand.) How many different parallelograms can you draw based on the given conditions?

Part B
Using the given information, can you determine the lengths of all the sides of the parallelogram? If so, what are the side lengths?

Part C
Using the given information, can you determine the measurements of all the angles of the parallelogram? If so, what are the angle measurements? Use a protractor, if necessary.

Part D
What is the relationship between adjacent angles in the parallelogram?

Part E
Given two side lengths and an angle measurement, how many parallelograms can be constructed that fit the conditions?