new 6-1 7-1 properties and attributes of polygons · 2017. 1. 9. · 6-1 properties and attributes...

Holt McDougal Geometry

6-1 Properties and Attributes of Polygons

Warm Up

1. A ? is a three-sided polygon.

2. A ? is a four-sided polygon.

Evaluate each expression for n = 6.

3. (n – 4) 12

4. (n – 3) 90

Solve for a.

5. 12a + 4a + 9a = 100

triangle

quadrilateral

24

270

4

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To find and use the measures of interior and exterior angles of polygons.

Learning Targets

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side of a polygon

vertex of a polygon

diagonal

regular polygon

concave

convex

Vocabulary

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A polygon is a closed plane figure formed by three or more segments.

What is a polygon?

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Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

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You can name a polygon by the number of its sides. The table shows the names of some common polygons.

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Example 1A: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.

polygon, hexagonpolygon, heptagon

not a polygon

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Check It Out! Polygon or Not Polygon?

Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.

not a polygon

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N.B.If a polygon is not regular, it is called irregular.

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Three Types of polygon:

Equilateral polygons – all sides are equal.

Regular polygons – both equilateral & equiangular.

Equiangular polygons – all angles are equal.



A polygon is concave – If it caves in, it is concave.

A polygon is convex – If it does not cave in, it is

convex.

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There are 2 shapes of regular polygons:



Example 2A: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

irregular, convex

regular, convex

irregular, concave

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Check It Out! Example 2a

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

regular, convex

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To find the sum of the interior angle measures of a convex polygon, draw

all possible diagonals from one vertex of the polygon. This creates a set

of triangles. The sum of the angle measures of all the triangles equals the

sum of the angle measures of the polygon.

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6-1 Properties and Attributes of Polygons7-1



The formula of the sum of the angle measures of all these triangles is (n — 2)180°.

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Example 3B: Finding Interior Angle Measures and

Sums in Polygons

Find the measure of each interior angle of a regular 12-gon. n =12.

Step 1 Find the sum of the interior angle measures.

Step 2 Find the measure of one interior angle.

(12 – 2)180° = 1800°

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1800°/12 =150°



Finding Interior Angle Measures and Sums in

Polygons

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Polygons

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Try this one:

Find the sum of the interior angle measures of the

following convex polygons and one interior angle.

13 - gon, n=13




Polygons

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Polygons

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Try this one:

The sum of the measures of the interior angles

of a convex polygon is 1200 deg. Classify the

number of sides.




Polygons

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Polygon Interior Angles Theorem

The sum of the measures of interior angles of a quadrilateral is 360 degrees.

Find the value of x.




Polygons

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Exterior Angles of Polygon:

The sum of the exterior angle measures is 360°.

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Example 4A: Finding Interior Angle Measures and

Sums in Polygons

Find the measure of each exterior angle of a regular 20-gon.

The measure of each exterior angle of a regular 20-gon is 18°.

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Example 4A: Finding Interior Angle Measures and

Sums in Polygons

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Check It Out! Example 4b

Find the value of r in polygon JKLM.

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Try this one:



Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A)Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21

new 6-1 7-1 properties and attributes of polygons · 2017. 1. 9. · 6-1 properties and attributes...

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