Geometry Standard 12 Interior Angle Theorem. Standard and Rationale Matchbook Definition: Students use measures of sides and interior angles of polygons.

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Presentation transcript:

Geometry Standard 12 Interior Angle Theorem

Standard and Rationale Matchbook Definition: Students use measures of sides and interior angles of polygons to solve problems. Rationale Tested on CST and SAT Necessary for calculating area, surface area and volume Architecture and tiles (tessellation).

Concept Map

What is the measure of the sum of the Interior Angles of a Triangle? 180 

What is the measure of the sum of the Interior Angles of a Quadrilateral? Two Triangles 180  each 360  total

Students Open Mystery Packets 5 Sides 3 Triangles 540  8 Sides 6 Triangles 1080 

Students Fill in Table Number of Sides 345r5i6r6i8r8i10r10in Number of Triangles Sum of Angles

Discuss Discoveries Compare and contrast figures with the same number of sides. Does the difference affect the number of triangles? Does the difference affect the sum of the interior angles?

Answer Resource Sheet Questions with Group 1.What is the relationship between the number of sides of a polygon and the number of triangles that can be drawn from one vertex of the polygon? Express your answer in words and as an algebraic expression.

Answer Resource Sheet Questions with Group 2.What is the relationship between the number of triangles that can be drawn from one vertex of the polygon and the sum of the interior angles of the polygon? Express your answer in words and as an algebraic expression.

Answer Resource Sheet Questions with Group 3.If I have a 93 sided polygon, how many triangles can be drawn from one vertex? What is the sum of the interior angles?

Answer Resource Sheet Questions with Group 4. If I have a z-sided polygon, how many triangles can be drawn from one vertex? What is the sum of the interior angles?

Discuss Resource Questions Possible Teacher Questions Would Group X like to explain their answer to Question 1, 2, 3, 4? What evidence do you have that “…….” Is true? If you have a regular polygon, how can you find the measure of just one of the interior angles?

Guided Practice x x x x x x Find x.

Guided Practice k Find k.

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