Transcript Chapter 6 Lesson 3

Chapter 6 Lesson 3
0011 0010 1010 1101 0001 0100 1011
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Objective: To determine
whether a quadrilateral is a
parallelogram.
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4
Theorem 6-5
0011 0010 1010 1101 0001 0100 1011
If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram.
Theorem 6-6
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If one pair of opposite sides of a quadrilateral is
both congruent and parallel, then the quadrilateral
is a parallelogram.
Example 1:
Finding Values for Parallelograms
Find values of x and y for which MLPN must be a
0011 0010 1010 1101 0001 0100 1011
parallelogram.
2y  7  y  2
y 7 2
y 9
3x  x  5
2x  5
5
x 
2
1
2
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Example 2: Finding Values for Parallelograms
Find values of a and c for which PQRS must be a
0011 0010 1010 1101 0001 0100 1011
parallelogram.
a  a  40  180
2a  140
a  70
3c  3  c  1
2c  4
c 2
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Theorem 6-7
0011 0010 1010 1101 0001 0100 1011
If both pairs of opposite sides of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.
Theorem 6-8
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If both pairs of opposite angles of a quadrilateral
are congruent, then the quadrilateral is a
parallelogram.
Example 3:
Is the Quadrilateral a Parallelogram?
Based on the information given, can you determine
the quadrilateral
0011 0010that
1010 1101
0001 0100 1011 must be a parallelogram?
Explain.
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Yes, both pairs of
opposite angles are
congruent.
2
4
No, the figure could
be a kite.
Example 4:
Is the Quadrilateral a Parallelogram?
Based on the information given, can you determine
the quadrilateral
0011 0010that
1010 1101
0001 0100 1011 must be a parallelogram?
Explain.
1
Yes, a pair of
opposite sides are
parallel and
congruent.
2
4
No, the figure could
be a trapezoid.
Assignment
0011 0010 1010 1101 0001 0100 1011
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Pg. 308
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#1-15; 26-29