Lesson Activity Print
Quadrilateral Constructions
This activity will help you meet these educational goals:
Mathematical Practices--You will make sense of problems and solve them, reason abstractly and quantitatively, and use appropriate tools strategically
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work
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?

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

you have to wait a while to reward brainliest if only one person answers. if 2 people answer there should be a "mark brainliest" on their question.

i cant fully remember all of the ranks, here are the ones i remember.

hand, ambitous, ace, genius.

agree

step-by-step explanation:

b is the correct answer