Geometry 6-1 Complete Lesson: The Polygon-Angle Sum Theorems

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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Geometry 6-1 Complete Lesson: The Polygon-Angle Sum Theorems

Geometry 6-1 Complete Lesson: The Polygon-Angle Sum Theorems

Solve It! Sketch a convex pentagon, hexagon, and heptagon. For each figure, draw all the diagonals you can from one vertex. What conjecture can you make about the relationship between the number of sides of a polygon and the number of triangles formed by the diagonals from one vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It?

Reasoning: Which angles are the exterior angles for ∠1? Select all that apply.

Error Analysis: Your friend says that she measured an interior angle of a regular polygon as 130. Explain why this result is impossible.

Review Lesson 5-7: You are given the following information.Which is greater, AD or CD ?

Review Lesson 2-5: Name the property that justifies the statement.

Review Lesson 2-5: Name the property that justifies the statement.

Review Lesson 2-5: Name the property that justifies the statement. If ∠1 ≅ ∠4, then ∠4 ≅ ∠1.

Review Lessons 4-1 & 4-3: Name the postulate or theorem that justifies the congruence statement.

Review Lessons 4-1 & 4-3: Use the diagram above to complete each congruence statement.

Vocabulary Review: Select the correct word to complete the sentence.In a convex polygon, no point on the lines containing the sides of the polygon is in the interior/exterior of the polygon.

Vocabulary Review: Cross out the polygon that is NOT convex.

Use Your Vocabulary: Match words from the left column to complete the sentences on the right.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular. Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular. Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.Enter only the most specific term with no spaces.

Reflection: Math Success

Solve It! Sketch a convex pentagon, hexagon, and heptagon. For each figure, draw all the diagonals you can from one vertex. What conjecture can you make about the relationship between the number of sides of a polygon and the number of triangles formed by the diagonals from one vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

Problem 4 Got It?

Reasoning: Which angles are the exterior angles for ∠1? Select all that apply.

Reasoning:What do you know about the measures of the exterior angles for ∠1?

Error Analysis: Your friend says that she measured an interior angle of a regular polygon as 130. Explain why this result is impossible.

Review Lesson 5-7: You are given the following information.Which is greater, AD or CD ?

Review Lesson 2-5: Name the property that justifies the statement.

Review Lesson 2-5: Name the property that justifies the statement.

Review Lesson 2-5: Name the property that justifies the statement. If ∠1 ≅ ∠4, then ∠4 ≅ ∠1.

Review Lessons 4-1 & 4-3: Name the postulate or theorem that justifies the congruence statement.

Review Lessons 4-1 & 4-3: Use the diagram above to complete each congruence statement.

Vocabulary Review: Select the correct word to complete the sentence.In a convex polygon, no point on the lines containing the sides of the polygon is in the interior/exterior of the polygon.

Vocabulary Review: Cross out the polygon that is NOT convex.

Use Your Vocabulary: Match words from the left column to complete the sentences on the right.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular. Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular. Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.Enter only the most specific term with no spaces.

Reflection: Math Success

Reasoning:What do you know about the measures of the exterior angles for ∠1?

Review Lesson 5-7: You are given the following information.
Which is greater, AD or CD ?

Review Lesson 2-5: Name the property that justifies the statement.
If ∠1 ≅ ∠4, then ∠4 ≅ ∠1.

Vocabulary Review: Select the correct word to complete the sentence.
In a convex polygon, no point on the lines containing the sides of the polygon is in the interior/exterior of the polygon.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.

Review Lesson 5-7: You are given the following information.
Which is greater, AD or CD ?

Review Lesson 2-5: Name the property that justifies the statement.
If ∠1 ≅ ∠4, then ∠4 ≅ ∠1.

Vocabulary Review: Select the correct word to complete the sentence.
In a convex polygon, no point on the lines containing the sides of the polygon is in the interior/exterior of the polygon.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.

Use Your Vocabulary: Classify the hexagon as equiangular, equilateral, or regular.
Enter only the most specific term with no spaces.