6-1 The Polygon Angle-Sum Theorems, Study notes of Biology

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Do Now Exit Ticket Lesson Presentation

Do Now #

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. 12 a + 4 a + 9 a = 100

SWBAT

Classify polygons based on their sides and angles.

Find and use the measures of interior and exterior

angles of polygons.

By the end of today’s lesson, Connect to Mathematical Ideas (1)(F)

equiangular polygon

equilateral polygon

regular polygon

number sense

Vocabulary

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.

A polygon is concave if any part of a diagonal

contains points in the exterior of the polygon. If no

diagonal contains points in the exterior, then the

polygon is convex. A regular polygon is always

convex.

A polygon is a closed plane figure formed by

three or more segments that intersect only at

their endpoints.

Remember!

By the Triangle Sum Theorem, the sum of the

interior angle measures of a triangle is 180°.

Remember!

What is the sum of the interior angle measures of a heptagon? Example 1: Finding a Polygon Angle Sum S n = ( n – 2) o Polygon Angle-Sum Theorem = ( 7 – 2)180^ Substitute 7 for n o = (5)180^ Simplify o S n = 900 o The sum of the interior angle measures of the heptagon is 900 o .

Example 2: Using the Polygon Angle-Sum

Biology The common housefly, Musca domestica , has eyes

that consist of approximately 4000 facets. Each facet is a regular hexagon. What is the measure of each interior angle in one hexagonal facet? =

𝐨 𝑛 m (each  ) =

𝐨 6 =

𝐨 6 The measure of each interior angle is 120 o .

Example 4: Investigating the Exterior Angles of Polygons Which of the following tools would be appropriate to use for investigating the exterior angles of polygons? Explain your choice.  Ruler  Protractor  Graphing Calculator  Ruler  Protractor  Graphing Calculator

because protractors are use to measure angles

Example 4: Investigating the Exterior Angles of Polygons Draw an exterior angle at each vertex of three different polygons. Investigate patterns and write a conjecture about the exterior angles. Step 1 : Draw three different polygons. Then draw the exterior angles at each vertex of the polygons as shown.