6.3 Prove Quads a Parallelogram.notebook
Warm up
L
O
1060
1. What is m∠O in LMNO?
December 05, 2014
6­3 Proving That a Quadrilateral is a Parallelogram
M
N
Objective: You will write a justification for determining whether a quadrilateral is a parallelogram.
H
E
2. Solve a system of linear equations 2a
1
6b ­
to find the values of a and b in EFGH. 3b
+
3
2
2a +
What are the measures of EG and FH?
G
F
3. If MO = 29.5, what is MN?
G
H
J
K
L
M
N
O
P
Q
1) Definition of a Parallelogram
If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.
Parallelogram or not?
3) If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram
2) If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram
Parallelogram or not?
Parallelolgram or not?
4) If an angle is supplementary to both its consecutive angles, then the quadrilateral is a parallelogram
x
180-x
5) If the diagonals bisect each other, then the quadrilateral is a parallelogram
180-x
C
75
Parallelogram or not?
750
1050
0
Parallelogram or not?
B
H
D
A
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6.3 Prove Quads a Parallelogram.notebook
6) If one pair of sides is both congruent and parallel, then the quadrilateral is a parallelogram
December 05, 2014
Can you prove that the quadrilaterals are parallelograms based on the given information? Explain.
Parallelogram or not?
Determine whether the given information is sufficient to prove that quadrilateral WXYZ is a parallelogram.
For what value of x and y must ABCD be a parallelogram?
For what value of x and y must ABCD be a parallelogram?
For what value of x and y must ABCD be a parallelogram?
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6.3 Prove Quads a Parallelogram.notebook
Draw the correct diagram for each method.
Pair­share
December 05, 2014
Lesson Check
Formative Assessment
For what value of y must LMNP be a parallelogram?
Determine whether the given information is sufficient to prove that quadrilateral ABCD is a parallelogram.
Assignment: 6.3 # 7-15, 21-24, 31-35
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