| Angles of Convex Polygons |
Grade:
High School |
Content Area:
Geometry |
Time Frame:
60-90 minutes |
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Unit/Lesson Overview:
The purpose of this lesson is to investigate the sum of the interior and exterior angles of any convex polygon, and determine a mathematical relationship between the number of sides and the sum of the interior angles of any convex n-gon.
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Student Standards (TEKS)
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explanation of a TEK, click on the TEK |
| Language Arts: |
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| Math: |
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| Social Studies: |
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| Science: |
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| Technology: |
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| Geometry: |
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| Additional TEKS: |
Geometry: b2B, c1, e2B
Technology: c1, c2 |
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I Can....
Determine the sum of the interior angles of any convex polygon.
Determine the sum of the exterior angles of any convex polygon.
Use numeric and geometric patterns to make generalizations about the angle relationships of polygons. |
Assessment(s):
None assigned.: |
TAKS Objectives:
| Reading: |
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| Writing: |
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| Math: |
Obj 1; Obj 2 |
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Bloom's Taxonomy
| Yes |
Knowledge |
| Yes |
Comprehension |
| Yes |
Application |
| Yes |
Analysis |
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Synthesis |
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Evaluation |
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Big 6 Skills
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Task
Definition |
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Info. Seeking
Strategies |
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Location and
Access |
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Use of Information |
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Synthesis |
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Evaluation |
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Supplementary Resources / Materials:
Student Handout (optional)
Sketchpad file (Angles of polygons)
File: angle investigation for convex polygons.doc
File: Angles of Polygons.gsp
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Internet Links:
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Accommodations:
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| Procedures |
Introductory Activity (Warm-Up):
Use the Warm Up page to review the concept of polygon figures and not polygon figures.
Define convex and non-convex polygons using sketchpad to demonstrate the difference between the types.
Review concept of regular and non-regular polygons |
Lesson:
Use the triangle sketch to investigate the relationship of the sum of all interior and exterior angles of any shape triangle, quadrilateral, pentagon, and hexagon; provide 2-3 minutes for each polygon and have students write down they findings for questions 1-4.
Have students determine the relationship between the number of sides of a polygon and the sum of the interior angles; provide about 5 minutes. Have students explain to you how they arrived to the equation, and verify it using the graphing calculator. Test their equation using their know values for pentagons, hexagons, etc.
What are the limitations of the
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Reteach:
In this lesson the students will need to be able to find a linear equation of a set of data. This can be done either using the graphing calculator or algebraically; preferably both.
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Extension:
Q5.Can you find a formula to determine the measurement of each interior angle of a regular n-gon
Extension question.
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Guiding Questions:
Q5. Why does the sum of all the exterior angles of any convex polygon always adds to 360 degrees?
Q5. Will your results change if the polygons are regular?
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Summary Questions:
In your own words, describe the difference between a convex polygon and a non-convex polygon.
Why does the sum of all exterior angles of a convex polygon always add to 360 degrees?
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Reflection:
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