Chpt 9 - Angles, Triangles & Polygons

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-1 CHAPTER 9 9.1 ANGLES AND PLANE FIGURES

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-2 Example 1

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-3 9.2 ANGLE PROPERTIES OF POLYGONS No. of sides (or vertices) Name of polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon n n-gon 1. Sum of interior angles of a polygon = (n – 2) × Ο180 Where n = number of sides. 2. Sum of exterior angles of a polygon = Ο360 3. 1 Exterior Angle + 1 Interior Angle = Ο180 (adj. s∠ on a str. line) A regular polygon has all its sides equal and all its angles equal. Example 2 Each interior angle of a regular polygon is Ο140 . How many sides does it have?

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-4 Example 3 9.3 SIMILAR TRIANGLES Two triangles are similar if one of the following is true: 1. Corresponding angles are equal (AAA). (In fact ,if two of the pairs of corresponding angles are equal, hen the third pair must be equal.) 2. Corresponding sides are in the same ratio. 3. Two pairs of corresponding sides are in the same ratio and the angles included between them are equal. 9.4 AREAS AND VOLUMES OF SIMILAR FIGURES For two similar figures, 1F and 2F , we have the following: 1. The ratio of their areas is the square of the ratio of their corresponding engths. ie. 2 2 1 2 1      = l l A A 2. The ratio of their volumes is the cube of the ratio of their corresponding lengths. ie. 3 2 1 2 1      = l l V V

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-5 Example 4 9.5 ANGLE BISECTORS AND PERPENDICULAR BISECTORS

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-6 TUTORIAL 9

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-7 4. 5. 6. ABCDEF is a hexagon. The angles A, B, C, D,E and F are Ο140 , Οx4 , Ο130 , Οx6 , Οx2 and Ο150 . Calculate the value of x.

ANGLES, TRIANGLES & POLYGONS Mathematics Preparatory Course for Direct Entry to Higher Nitec 9-8 7.* 8.* CHALLENGING QUESTION 1. FIGURE 1 2. FIGURE 2 A 2,500 N weight is resting on an inclined plane that makes an angle of Ο23 with the horizontal. Find the component xF and yF of the weight parallel to and perpendicular to the surface of the plane, as shown in Figure 1. A roof that slopes at Ο23 to the horizontal is 14.5 m long and has a slant height of 9.2 m. How large an area does the roof actually cover? (Hint: Find the area of rectangle ABCD in Figure 2)