Unit 1C3 Day 1 Polygons. Do Now  The symbols here are used in meteorology to represent weather elements.  Which of them pass both tests below?  Test.

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Presentation transcript:

Unit 1C3 Day 1 Polygons

Do Now  The symbols here are used in meteorology to represent weather elements.  Which of them pass both tests below?  Test 1: It is made up of straight line segments only.  Test 2: Each line segment intersects exactly two others, one at each endpoint.

Drawing Conclusions  A shape that passes both tests is called a polygon.  The symbols here are used to write flow charts for computer programs. Which symbols are polygons?

 Polygon : a plane figure that meets the following conditions:  It is formed by 3 or more segments called _______.  Each side intersects exactly two other sides, one at each endpoint, called a ___________. Describing Polygons

Ex. 1: Identifying Polygons  State whether the figure is a polygon. If it is not, explain why.

# of sidesType 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon # of sidesType 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon Naming Polygons

Concavity  If you extend the sides of a polygon, and none of the lines cross into its interior, then it is considered convex.  If you extend the sides of a polygon, and at least one of the lines crosses into its interior, then it is considered concave.

Ex. 2: Identifying Convex and Concave Polygons  Classify the polygon by its number of sides  State whether it is convex or concave.

 A polygon is ________________________ if all of its sides are congruent.  A polygon is _________________________ if all of its interior angles are congruent.  A polygon is __________________ if it is both equilateral and equiangular.  Unless it’s a triangle, equilateral and equiangular are not mutually exclusive! More Vocab.

Decide whether the following polygons are regular. Ex. 3: Identifying Regular Polygons

More Vocab.  A diagonal of a polygon is a segment that joins two nonconsecutive vertices.  Polygon PQRST has _____ diagonals from point Q: _______ and ________

Interior Angles of a Quadrilateral  If you draw a diagonal in a quadrilateral, you divide it into two ____________  Each has interior angles sum up to _______.  So the sum of the measures of the interior angles of a quadrilateral is 2*______ or ________

Thm. 6.1: Interior Angles of a Quadrilateral  The sum of the measures of the interior angles of a quadrilateral is 360°. m  1 + m  2 + m  3 + m  4 = 360°

Ex. 4: Interior Angles of a Quadrilateral  Find the value of x.  Find m  Q and m  R.

More Examples

 Define "polygon" in terms of the way its sides intersect. Closure