1. No category

Name
6-3
Class
Date
Practice
Form K
Proving That a Quadrilateral Is a Parallelogram
Algebra For what values of x and y must ABCD be a parallelogram?
1.
To start, write an equation that
relates the lengths of opposite sides
that have algebraic expressions with
the same variable.
3x − 5 =
2.
3.
4.
5.
Can you prove the quadrilateral is a parallelogram based on the given
information? Explain.
6.
7.
8.
9.
10. Reasoning A classmate drew a quadrilateral with two diagonals. This divided the
figure into four isosceles triangles. Is the quadrilateral a parallelogram? Use a drawing
to justify your answer.
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Name
Class
6-3
Date
Practice (continued)
Form K
Proving That a Quadrilateral Is a Parallelogram
11. Developing Proof Complete this two-column proof of Theorem 6-8.
Given: AB ≅ CD and BC ≅ DA
Prove: ABCD is a parallelogram.
Reasons
Statements
1) Draw diagonal.
1) Definition of a diagonal
2) AB ≅ CD and BC ≅ DA
2)
3) AC ≅ AC
3)
4) ∆ABC ≅
4)
5) ∠B≅
5)
6) Draw diagonal BD .
6) Definition of a diagonal
7) BD ≅ BD
7)
8) ∆BCD ≅
8)
9) ∠A ≅
9)
10) ABCD is a parallelogram.
10)
12. Error Analysis A classmate said that a quadrilateral is a parallelogram
only if one angle is supplementary to all the others. What is your classmate’s
error? Explain.
For what values of the variables must ABCD be a parallelogram?
13.
14.
15.
16.
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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
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