8三角形与多边形的角.pdf

中二數學教學筆記 Chapter 08 Angles in Triangles and Polygons 三角形及多邊形的角 New Century Mathematics Oxford Canotta Maths Section Topic Teaching Notes Classwork or Homework 8 1 Angles and Sides of a Triangle Students should be able to distinguish interior angle 內角 and exterior angle 外 角 Students should be able to label the vertical angle 頂角 and the base angles 底角 of an isosceles triangle 等腰三角形 Students should be able to calculate and give reasons 1 sum of 2 ext of 3 base s isos 4 prop of eq Students should be able to prove a triangle to be isosceles sides opp eq s Ex 8A Q 2 9 14 15 Ex 8B Q 1 12 Ex 8B Q 14 16 Ex 8B Q 32 8 2 Angles of a Polygon For convex polygons 凸多邊形 students should be able to calculate and give reasons 1 sum of polygon 2 sum of ext s of polygon Ex 8C 1 11 12 15 29 30 Ex 8D Q 1 12 8 3 Basic Constructions Students should be able to use a pair of compasses and straight edge only and construct 1 angle bisector 角平分線 2 perpendicular bisector 垂直平分線 3 special angles 90o 45o 60o 30o 4 regular polygons equilateral triangle square regular pentagon and regular hexagon Ex 8E Q 2 Ex 8E Q 3 Ex 8E Q 5 8 Ex 8E Q 17 18 Supplementary Material PowerPoint for Constructing Regular Polygons 問題一 有那幾種正多邊形能密鋪平面 3 種 等邊三角形 正方形 正六邊形 問題二 若使用兩種正多邊形來密鋪平面 a 正五邊形可和甚麼正多邊形合鋪平面 b 正八邊形可和甚麼正多邊形合鋪平面 十邊形 正四邊形 正方形 問題三 有多少種柏拉圖立體 Platonic solid 5 種 三角形面 4 面體 8 面體 20 面體 四角形面 6 面體 五角形面 12 面體 Chapter 08 Angles of Triangles and Polygons Quiz 08 1 F 2 Name Marks 25 1 According to the figure which of the following must be true A a b c d B a d b c C a b c d 360o D a b c d 540o E 2a 2b c d 720o 2 In the figure ABCD is a trapezium with AB DC AH bisects BAD and DH bisects ADC Which of the following must be true AHD 90o ADC BCD BAD BCD 180o A only B only C only D and only E and only 3 In the figure x A 50o B 60o C 70o D 90o 4 According to the figure which of the following must be true A a b c B a b c 90o C a c b 540o D a b c 720o 5 In the figure AY and CY are the angle bisectors of BAX and DCX respectively If AXC 100o then AYC A 40o B 50o C 60o D 80o 6 In the figure x A 50o B 55o C 60o D 65o E 70o 7 In the figure a b c d e f A 270o B 360o C 450o D 540o E 720o 8 If each interior angle of a regular n sided polygon is 144o then n A 10 B 12 C 14 D 16 9 In the figure ABCDE is a regular pentagon and ABFG is a square Find x A 18o B 27o C 30o D 36o E 45o 10 Find the value of x 3 marks 11 Find the value of x in the following figure 5 marks 12 Find the smallest interior angle of the pentagon ABCDE if A B C D E 2 3 4 5 6 4 marks 13 Note No reasons are required in this question The size of each interior angle of an equiangular convex polygon is greater than each exterior angle by 132o Find the number of sides 4 marks 100o 120o xo 360o sum of ext s of polygon x 140 Join CE In CDE DCE DEC 155o 180o sum of DCE DEC 25o In quadrilateral ABCE 120o xo 55o DCE DEC 35o 4 2 180o sum of polygon x 120 55 35 25 360 x 125 Let the size of A be 2ko 2k 3k 4k 5k 6k 5 2 180 sum of polygon 20k 540 k 27 Size of smallest angle A 54o Let the size of an exterior angle of the equiangular polygon be xo 180 x x 132 x 24 Number of sides 360 24 15 Chapter 08 Angles of Triangles and Polygons Quiz 08 S F 2 Name Marks 14 1 The sizes of ABD and BDE are 110o and 120o respectively Find the sizes of CBD and BCD A B E D C 6 marks 2 Find the sum of all the marked angles in the following figure 4 marks 3 If QPS is a right angle PQR 36o QRS 3xo and RSP xo Find the value of x P R Q S 4 marks CBD ABD 180o adj s on st line CBD 70o In BCD BDE CBD BCD ext of 120o 70o BCD BCD 50o In AEI IAE AEI