Parallelograms

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Parallelograms
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Objectives

• Recognize and apply properties of the sides and
  angles of parallelograms.
• Recognize and apply properties of the diagonals
  of parallelograms.

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Parallelograms

• A quadrilateral with parallel opposite sides is
  called a parallelogram ( ABCD).

A
B
D
C
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Parallelograms Theorems

• Theorem 6.3 Opposite sides of are ?.
• Theorem 6.4 Opposite ?s in are ?.
• Theorem 6.5 Consecutive ?s in are
  supplementary.
• Theorem 6.6 If has 1 rt. ?, then it has 4
  rt. ?s.

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Example 1
Prove that if a parallelogram has two consecutive
sides congruent, it has four sides congruent.
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Example 1
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Your Turn
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Your Turn
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Example 2
Definition of congruent angles
Substitution
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Example 2
Angle Addition Theorem
Substitution
Subtract 58 from each side.
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Example 2
Definition of congruent segments
Substitution
Divide each side by 3.
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Your Turn
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Diagonals of Parallelograms

• Theorem 6.7 The diagonals of a bisect
  each other.
• Theorem 6.8 Each diagonal of a separates
  the into two ? ?s.

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Example 3
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Example 3
Solve the Test Item
The coordinates of the intersection of the
diagonals of parallelogram MNPR are (1, 2).
Answer C
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Your Turn
Answer B