Transcript 6.3 Proving that a Quadrilateral is a Parallelogram

5.1 warm-up
Suppose the line shown is translated 2
units to the left and 1 unit down.
Which point would lie on the
translated line ?
3
a. (-2,-2)
b. (-1,1)
c. (0,2)
d. (2,3)
y
2
1
-3 -2 -1 0
1
2
3 x
-3
6
6.3 Proving that a Quadrilateral is a
Parallelogram
Pardekooper
What makes a quadrilateral a
parallelogram?
• 1. Opposite sides
are congruent
• 2. Opposite angles
are congruent
• 3. Diagonals bisect
each other
Pardekooper
Now, we look at some
theorems
• If both pairs of opposite sides of
a quadrilateral are congruent,
then the quadrilateral is a
parallelogram.
Pardekooper
Now, we look at some
theorems
• If both pairs of opposite angles
of a quadrilateral are congruent,
then the quadrilateral is a
parallelogram.
Pardekooper
Now, we look at some
theorems
• If the diagonals of a quadrilateral
bisect each other, then the
quadrilateral is a parallelogram,
Pardekooper
Now, we look at some
theorems
• If the one pair of opposite sides
of a quadrilateral are both
congruent and parallel, then the
quadrilateral is a parallelogram.
Pardekooper
Lets try a proof
• Given: ABDCDB, BDADBC, AC
• Prove: ABCD is a parallelogram
Statement
A
B
ABDCDB,
BDADBC
AC
ABD+CBD
CDB+ADB
ABCD is a
parallelogram
D
C
Reason
•Given
Addition
If opposite ’s  ,
then parallaogram
Pardekooper
OK, here comes a problem.
ABCD is a parallelogram. Solve for X & Y.
A
B
3X = X+3.2
- 1X - 1X
3Y = Y+2
- 1Y - 1Y
2X = 3.2
2
2
2Y = 2
2
2
Y=1
X = 1.6
D
C
Pardekooper
Just one more problem
ABCD is a parallelogram. Solve for m & k.
A
m = 2.6k
m+9.1 = 4k-3.5
B
2.6k+9.1 = 4k-3.5
- 4k
- 4k
-1.4k+9.1 = -3.5
- 9.1 - 9.1
m = 2.6(9)
m = 23.4
substitution
-1.4k = -12.6
-1.4
-1.4
D
k=9
C
substitution
Pardekooper
And now the assignment.
Pardekooper
Assignment
Workbook
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