Chapter 6 Lesson 2

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Chapter 6 Lesson 2

• Objective To use relationships among diagonals,
  angles and sides of parallelograms.

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Properties of Parallelograms
Theorem 6-1 Opposite sides of a parallelogram are
congruent.
Angles of a polygon that share a side are
consecutive angles. A parallelogram has opposite
sides parallel. Its consecutive angles are
same-side interior angles so they are
supplementary. In    ABCD, consecutive angles B
and C are supplementary, as are consecutive
angles C and D.
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Example 1 Using Consecutive Angles
Find m   S in     RSTW .                
  R and   S are consecutive angles of a
parallelogram. They are supplementary.
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Example 2 Using Consecutive Angles
Find m   O in     KMOQ .                
  Q and   O are consecutive angles of a
parallelogram. They are supplementary.
K
M
35
O
Q
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Theorem 6-2 Opposite angles of a parallelogram
are congruent.
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Example 3 Using Algebra
Find the value of x in      PQRS. Then find QR
and PS. 
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Example 4 Using Algebra
Find the value of y in parallelogram EFGH.
                                 
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Theorem 6-3 The diagonals of a parallelogram
bisect each other.
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Example 5 Using Algebra
Solve a system of linear equations to find the
values of x and y in       ABCD. Then find AE,
EC, BE, and ED.
Step 1 Write equations.
Diagonals bisect each other.
Step 2 Solve for a variable and Substitute
Step 3 Solve for variables
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Example 6 Using Algebra
Find the values of a and b.                    
      
Step 1 Write equations.
Diagonals bisect each other.
Step 2 Solve for a variable and Substitute
Step 3 Solve for variables
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Theorem 6-4 If three (or more) parallel lines cut
off congruent segments on one transversal, then
they cut off congruent segments on every
transversal.                           
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Assignment
Pg. 297 1-55