Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5....
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Transcript of Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5....
![Page 1: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/1.jpg)
Geometry
• Agenda
1. ENTRANCE
2. Go over Practice
3. Quiz
4. 3-4 The Polygon Angle-Sum Theorems
5. Practice Assignment
6. EXIT
![Page 2: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/2.jpg)
Practice
![Page 3: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/3.jpg)
• Quiz Time
Good Luck!!!
![Page 4: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/4.jpg)
Chapter 3
3-4 The Polygon Angle-Sum Theorems
![Page 5: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/5.jpg)
Polygon
• A _______ figure that consists of three or more segments joined at the endpoints and each segment must meet exactly two other segments.
![Page 6: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/6.jpg)
Polygon Terms
• 3 sides Triangle• 4 sides Quadrilateral• 5 sides Pentagon• 6 sides Hexagon• 7 sides Heptagon• 8 sides Octagon• 9 sides Nonagon• 10 sides Decagon• 11 sides Undecagon• 12 sides Dodecagon• n sides n-gon
![Page 7: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/7.jpg)
Naming A Polygon
• A polygon is named by the number of _______.
ex: If a polygon has
___ sides, you use
___ letters.
Polygon ABCDE
![Page 8: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/8.jpg)
Types of Polygons
• Convex– The diagonals are entirely inside the figure.
• Concave– At least one diagonal is partly outside the
figure.
![Page 9: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/9.jpg)
Regular Polygon
• Remember: equilateral, equiangular
• A regular polygon is a polygon that is both equilateral and equiangular.
![Page 10: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/10.jpg)
Theorem 3-9Polygon Angle-Sum Theorem
• The sum of the measures of the angles of an n-gon is (n-2)180.
ex: This pentagon
has 5 sides.Sum = (n-2)180
Sum = (5-2)180
Sum = (3)180
Sum = 540
![Page 11: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/11.jpg)
Theorem 3-10Polygon Exterior Angle-Sum
Theorem
• The sum of the measures of the ________ angles of a polygon, one at each vertex, is 360.
ex: This pentagon has 5 sides.
The sum of the 5exterior angles is360.
![Page 12: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/12.jpg)
Example #1
• Name the ________. Identify vertices, sides, and angles. Is it concave or convex?
![Page 13: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/13.jpg)
Example #2
• Find the interior angle sum.
a. 13-gon b. decagon
![Page 14: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/14.jpg)
Example #3
• How many sides does each polygon have if its interior angle sum is:
a. 2700 b. 1080
![Page 15: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/15.jpg)
Example #4
• Find x.
![Page 16: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/16.jpg)
Example #5
• Find y.
![Page 17: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/17.jpg)
Example #6
• Find x.
![Page 18: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/18.jpg)
Example #7
• Find x.
![Page 19: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/19.jpg)
Example #8
• Find x.
![Page 20: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/20.jpg)
Example #9
• How many sides does each regular polygon have if its exterior angle is:
a. 120 b. 24
![Page 21: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/21.jpg)
Example #10
• How many sides does each regular polygon have if its interior angle is:
a. 90 b. 144
![Page 22: Geometry Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT.](https://reader036.fdocuments.us/reader036/viewer/2022062720/56649f045503460f94c18b9c/html5/thumbnails/22.jpg)
• Practice– WB 3-4 # 1-19
• EXIT