6.1 Polygons and 6.2 Properties of Parallelograms

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6.1 Polygons and6.2 Properties of
Parallelograms

• 2/14 and 2/15

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examples
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A polygon is a plane figure that is formed by
three or more segments called sides. Each
endpoint is a vertex of the polygon.

• A segment that joins two nonconsecutive vertices
  of a polygon is called a diagonal.

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Diagonals
Pick any ONE vertex then draw a line
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Are these figures polygons?????Yes or No. Why
or Why Not
NO
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Types of Polygons

• 3 sides ??? Triangle
• 4 sides ???? Quadrilateral
• 5 sides Pentagon
• 6 sides Hexagon
• 7 sides Heptagon
• 8 sides Octagon

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Quadrilateral Interior Angles Theorem

• The sum of the measures of the interior angles of
  a quadrilateral is 360

Time for 6.2
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A parallelogram is a quadrilateral with both
pairs of opposite sides parallel.
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Theorem 6.2If a quadrilateral is a
parallelogramthen its opposite sides are
congruent.
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Theorem 6.3If a quadrilateral is a
parallelogram, the its opposite angles are
congruent
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Theorem 6.4If a quadrilateral is a
parallelogram,then its consecutive angles are
supplementary
x y 180
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Theorem 6.5If a quadrilateral is a
parallelogram, then its diagonals bisect each
other
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Lets start filling out the worksheet
Characteristics Parallelogram
Both pairs of opposite sides parallel
Diagonals congruent
Both pairs of opposite sides congruent
At least one right angle
Both pairs of opposite angles congruent
Exactly one pair of opposite sides parallel
Diagonals perpendicular
Consecutive sides congruent
Consecutive angles congruent
Diagonals bisect each other
Diagonals bisect opposite angles
Consecutive angles supplementary
X
X
X
Memorize
X
X
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Before we move on take out your books and turn
to page 313
Do problems 1-12
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• Parallelogram

2. No, only one pair of sides is parallel.
3. yes
4.
10. 65
11. 9
12. 70