Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill...
Transcript of Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill...
![Page 1: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/1.jpg)
1
Polygons,
Quadrilaterals, and Special Parallelograms
![Page 2: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/2.jpg)
2
Name: ________________Date: _______ Per: ____
Chapter 6 (Section 1) – Day 1 Angles in polygons
A polygon is a closed plane figure formed by three or more segments that intersect only at their
endpoints.
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.
You can name a polygon by the number of its sides.
The table shows the names of some common polygons.
All the sides are congruent in an equilateral polygon. All the angles are congruent in an
equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a
polygon is not regular, it is called irregular.
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.
Warm – Up
Tell whether the following polygons are concave or convex and regular or irregular.
1. 2.
4.
3.
![Page 3: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/3.jpg)
3
Angles in Polygons
Fill in the accompanying table.
Polygon Number of
Sides
Number of
Triangles
Sum of Interior Angle
Measures
3
1
180
4
2
2 x 180 = 360
Heptagon
Octagon
Look for a pattern in the table. Write a rule for finding the sum of the measures
of the interior angles of a polygon with n sides.
![Page 4: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/4.jpg)
4
Examples:
1. Find the sum of the interior angles of a decagon.
2. What is the measure of each angle in a regular octagon?
Exterior Angles
Refer to the two polygons below. What do you notice about the exterior angles of
any polygon?
Examples:
3. Find the measure of each exterior angle of a polygon with 18 sides.
4. The measure of an exterior angle of a convex regular polygon is 36 . Find the number of
sides of the polygon.
![Page 5: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/5.jpg)
5
5. How many sides does a regular polygon have if each interior angle measures 160 ?
6. The sum of the interior angles of a convex regular polygon measure 1980 , how many
sides does the polygon have?
7. Find the value of x.
8. Find x:
![Page 6: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/6.jpg)
6
Summary
Homework
![Page 7: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/7.jpg)
7
![Page 8: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/8.jpg)
8
![Page 9: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/9.jpg)
9
Name: ________________Date: _______ Per: ____
Chapter 6 (Section 1) – Day 2 Angles in Polygons
8. 9. 10.
![Page 10: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/10.jpg)
10
Find the value of x.
11. 12. 14.
15. 16. 17.
18.
19.
![Page 11: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/11.jpg)
11
Find the measures of an exterior angle given the number of sides of each regular polygon.
27. 2160 28. 2880 29. 5760
20. 21. 23.
24. 25. 26.
![Page 12: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/12.jpg)
12
Name: ________________Date: _______ per: ____
Chapter 6 (Section 2) – Day 3 Parallelograms Homework: Worksheet
![Page 13: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/13.jpg)
13
Level A:
![Page 14: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/14.jpg)
14
Level B
20.
21.
Summary
Homework
![Page 15: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/15.jpg)
15
Homework
![Page 16: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/16.jpg)
16
Name: ________________Date: _______ per: ____
Chapter 6 (Section 4) – Day 4 Special Parallelograms Homework: Worksheet
Rectangles Definition: A rectangle is a parallelogram with one right angle.
![Page 17: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/17.jpg)
17
m 3 = 110 , find the measures of 1, 2, and
4.
![Page 18: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/18.jpg)
18
Practice Problems a. If AE = 5, BC = 6, and DC = 8, find AC, BD, AD, and AB.
b. If BD = 3x – 7 and CA = x + 5, find BD, ED, CA, and AE.
c.
d.
AC = _____
BD = _____
AD = _____
AB = _____
BD = _____
ED = _____
CA = _____
AE = _____
m 1 = _____
m 2 = _____
m 3 = _____
m 1 = _____
m 2 = _____
m 3 = _____
m 4 = _____
![Page 19: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/19.jpg)
19
Homework
![Page 20: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/20.jpg)
20
Name: ________________Date: _______ per: ____
Chapter 6 (Section 4) – Day 5 Special Parallelograms Homework: Worksheet
Warm - Up 1.
2.
Rhombus Definition: A rhombus is a parallelogram with 2 congruent consecutive sides.
Square
Definition: A square is a rectangle with 2 congruent consecutive sides.
m 1 = _____ m 5 = _____
m 2 = 40 m 6 = _____
m 3 = _____ m 7 = _____
m 4 = _____ m 8 = _____
![Page 21: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/21.jpg)
21
![Page 22: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/22.jpg)
22
__________
c.
The diagonals of a Rhombus are 10, and 24 cm. Find the length of
the side of the rhombus.
![Page 23: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/23.jpg)
23
Homework
4. ABCD is a square. If AD = 6, find each measure.
a) AE
b) BD
c) m AEB
d) m ACB
5. ABCD is a square. If m BEA = (2x – 1) and m BCE = 9y , find the value of x and y.
6.
7. The diagonals of a Rhombus are 16, and 30 cm. Find the length of the side of the rhombus.
![Page 24: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/24.jpg)
24
![Page 25: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/25.jpg)
25
![Page 26: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/26.jpg)
26
![Page 27: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/27.jpg)
27
![Page 28: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/28.jpg)
28
11.
12.
![Page 29: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/29.jpg)
29
![Page 30: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/30.jpg)
30
![Page 31: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/31.jpg)
31
11.
12.
ground. Find RA.
13. If PQ = 15, and SR = 9, find ST and PS.
![Page 32: Polygons, Quadrilaterals, and Special Parallelograms · 2018. 11. 30. · 3 Angles in Polygons Fill in the accompanying table. Polygon Number of Sides Number of Triangles Sum of Interior](https://reader033.fdocuments.in/reader033/viewer/2022053119/60a075fd8fe98f09b518f789/html5/thumbnails/32.jpg)
32