6-3 Practice Proving That a Quadrilateral Is a Parallelogram

Name
Class
Date
Practice
6-3
Form K
Proving That a Quadrilateral Is a Parallelogram
Algebra For what values of x and y must ABCD be a parallelogram?
1.
3x 5
A
7; 9
B
2y 6
y3
D
C
2x 2
2x 4
2. A
3x 2 5 5 9 2x 1 2
A
3.
3; 6
B
11
To start, write an equation that
relates the lengths of opposite sides
that have algebraic expressions with
the same variable.
2x 5
x9
y4
D
4. A
8x
D
C
(y 87)
4y
(7x 8)
12
2x 3
D
8; 29
B
B
5. A
D
C
8y
C
25; 10
10y
B
(4x 20)
C
Can you prove the quadrilateral is a parallelogram based on the given
information? Explain.
6.
7.
Yes; the diagonals bisect each other.
8.
9.
136
136
No; both sets of opposite
angles need to be congruent.
44
Yes; an angle is supplementary to
both of its consecutive angles.
No; the same pair of sides needs to
be both congruent and parallel.
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.
Yes; since all the sections of the diagonals are
congruent, the diagonals bisect each other and
the figure is a parallelogram.
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Name
Class
Date
Practice (continued)
6-3
Form K
Proving That a Quadrilateral Is a Parallelogram
11. Developing Proof Complete this two-column proof of Theorem 6-8.
A
Given: AB > CD and BC > DA
B
Prove: ABCD is a parallelogram.
C
D
Statements
1) Draw diagonal AC.
Reasons
1) Definition of a diagonal
2) AB > CD and BC > DA
2) 9 Given
3) AC > AC
3) 9 Reflexive Prop. of O
4) nABC > 9 kCDA
4) 9 SSS
5) /B > 9 lD
5) 9 CPCTC
6) Draw diagonal BD.
6) Definition of a diagonal
7) BD > BD
7) 9 Reflexive Prop. of O
8) nBCD > 9 kDAB
8) 9 SSS
9) /A > 9 lC
9) 9 CPCTC
10) ABCD is a parallelogram.
10) 9 Theorem 6-10
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. One l must be suppl. to both of its
consecutive '. The classmate is describing a rectangle, which is
one type of parallelogram.
For what values of the variables must ABCD be a parallelogram?
13.
4x 9
A
2y 3
D
15.
12; 14
B
14.
y 14
2x 1
A
B
(4x 8)
D
2y
3x 3
(7y 3)
D
C
C
4x 2
16. A
21.5; 39
(3y 15)
B
(2x 4)
6x 18
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26
B
9; 18
3y 22
D
C
3x 3
2y 2
A
7; 3
C