english math. II

Published on: **Mar 4, 2016**

Published in:
Education

- 1. POLYGONS and TESSELLATIONS By Citra Triwana Marpaung ACA 111 0050
- 2. Angles in Polygons The vertex angles of a polygons with four or more sides can be any size between 0˚ and 360˚. 180˚ 360˚
- 3. Example In the hexagon figure, we can known that, B is less than 20˚ and D and A are both greather than 180˚.
- 4. In spite of this range of possible size, there is a relationship between the sum of all the angles in polygon and its number sides. In any triangle, the sum of the three angle measures is 180˚. One way of demostrating that theorem is to draw an abitrary triangle and cut off its angles.
- 5. The sum of the angles in a polygon with four or more sides can be found by subdividing the polygon into triangels so that the vertices of the triangles are the vertice of the polygon. 1 2 3 4 5 6 In quadrilateral in that figure above is partitioned into two triangles. Thus, the sum of all angles (six angel of both the triangles) is 2 triangles x 180˚ = 360˚
- 6. However, since each the quadrilateral can be partitioned into triangles such that the vertices of triangles are also the vertices of a quadrilateral, the sum of the angles a quadrilateral will always be 360˚. Similar approach can be used to find the sum of the angles in any polygon. The total number of degrees in its angles is 3 x 180˚ = 540˚
- 7. Congruence The idea of Congruence is one figure can be placed on the other, so that they coincide. Another way to describe congruent plane figures is to say that they have same size and shape. Two line segments are congruent if they have the same length. And two angles are congruent if they have same measure..
- 8. Regular Polygons The figures in those photographs are examples of regular polygons. A polygon is called a regular polygon if it satisfies both of the folloeing conditions: 1. All angles are congruent. 2. All sides are congruent Regular pentagon Equilateral triangle square
- 9. Drawing Regular Polygons Three special angles in regular polygons. A vertex angle is formed by two adjacent sides of polygon A central angle is formed by connecting the centerof the polygon to two adjacent vertices of polygon
- 10. is formed by one side of the polygon and the extension of an adjacent sides. Exterior angle
- 11. The sum of the measures of the angles in a polygon can be used to compute the number of degrees in each vertex angle of a regular polygon; Simply divide the sum of all the measures of the angles by the number of angles. The sum angles in pentagon is 3 triangles x 180˚ = 540˚ Therefore, each angle in a regular pentagon is 540˚ 5 vertex angles = 108˚ 108˚ 108˚ 108˚108˚ 108˚
- 12. Steps of Drawing a Regular Polygon Step(1) Draw a line segment and mark a vertex Step(2) Measure off a 108˚ angle Step(3) Mark off two sides of equal length. 108˚ 108˚ Step(4) Measure off a second angle of 108˚
- 13. Antother approach to drawing regular polygons begins with a circle and uses central angles. The number of degrees in the central angle of a regular polygon is 360˚ devided by the number of sides in the polygon. Decagon 36˚ A decagonhas 10 sides, then each central angle is 360˚ 10 = 36˚ 36˚
- 14. Tessellation With Polygons Any arrangement in which no overlapping figures are placed together to entirely cover a region is called a tessellation. Floors and ceilings are often tesselated with square- shaped material, because squares can be joined together without gaps or overlaps A regular hexagon Squares Equilateral Triangle These three types that will tessellate by themselves
- 15. Tessellation with regular hexagon The points at which the vertices of the hexagon meet are the vertex points of the tessellation. 1 2 3 4 5
- 16. A tessellation of two or more noncongruent regular polygons in which each vertex is surrounded by the same arrangement of polygons, called SEMIREGULAR SEMIREGULAR NOT SEMIREGULAR
- 17. Problem Solving Application Consider a regular polygon with fewer sides. A regular hexagon has six congruent vertex angle, and since it can be partitioned into four triangles. What is the number of degrees in one of its vertex angles? What is the size of each vertex angles in hexagon? 4 x 180˚ = 720˚ 720˚ 6 = 120˚