2. ANGLE AND PLANE ANGLE AND PLANE Identify Angle

3. Adaptif Hal.: 2 ANGLE AND PLANE Determining position of line, and angle that involves point, line and plane in two-dimension. 1. Identifying angle. 2. Identifying the circumference of flat shape and width of flat shape. 3. Applying transformation of flat shape. ANGLE AND PLANE Standard Competence: Base Competence:

4. Adaptif Hal.: 3 ANGLE AND PLANE Kinds of Angle Unit Definition of Angle In taxonomy study, according to Gagne, angle is a base concept, so from several ways to define about angle, is that by one approach through line rotation as follows : Dinamai sudut BAB’ atau  BAB’ atau  A atau α B’ B Mentioned as angle BAB’ or  BAB’ or  A or α B’ B α

5. Adaptif Hal.: 4 ANGLE AND PLANE Angle in Base Position Kinds of Angle Unit θ Angle θ is not in base position X Y A C θ Angle θ is in base position Side AB is called beginning side from angle θ Side AC is called limit side from angle θ

6. Adaptif Hal.: 5 ANGLE AND PLANE Angle Size Kinds of angle unit Angle Size Seksagesimal Radial Sentisimal

7. Adaptif Hal.: 6 ANGLE AND PLANE Radial System Kinds of angle unit r 1 radian As motivation, it is told that in measuring elevation angle, Merriam shoot in military was needed angle size and didn’t use degree measurement, unless the other normal measurement we know as radiant system In radiant system the center angle size is of a circle that the length of busur in front of the angle is equal to radius of that circle. Then gotten a relation: 180 0 = π radian 1 radian radian

8. Adaptif Hal.: 7 ANGLE AND PLANE Kinds of Angle Unit Centesimal System  The instruments for astronomy, peneropongan bintang, teodolit known as different angle unit with both measurement above, this system is known centesimal system. A full rotation is 400 g in this system (read “400 grad”).  So the angle size ½ rotation is 200 g Angle size ¼ rotation is 100 g Angle size 1/400 rotation is 1 g For the smaller angle size known as :  1 g = 10 dgr = 10 ( read : “10 decigrad” )  1 dgr = 10 cgr = 10 (read : “10 centigrad”)  1 cgr = 10 mgr = 10 (read : “10 miligrad”)  1 mgr = 10 dmgr = 10(read :“10decimiligrad”)

9. Adaptif Hal.: 8 ANGLE AND PLANE Angle Conversion Conversion of angle size Degree Unit = radian unit = grad 360 0 = 2 radian = 400 g 1 radian = 57,325 0 = 63,694 g 1 0 = 0,0174 radian = 1,11 g 1 g = 0,90 = 0,0157 radian 1° = 60’ = 3600” second Example: Change 30 0 into radian unit and grade! Answer: 30 0 = 30 x 0,0174 radian = 0,522 radian 30 0 = 30 x 1,11 g = 33,3 g

10. Adaptif Hal.: 9 ANGLE AND PLANE Width and Circumference of flat shape 1. Triangle Width: L = ½ A x t Example: Where, A = base wide, t = tall A C B A C B 13 12 Calculate the width and circumference plane beside. Answer: AB = = = = = 24 A. The width place arranged plane

11. Adaptif Hal.: 10 ANGLE AND PLANE The width and circumference of flat plane Triangle width: L = = = = 84 Triangle circumference: K = AB + BC+ AC = 13 cm + 12 cm +5 So, the triangle width is 84 cm 2 and the circumference is 56 cm 1.1 If the triangle has side a, b, c and triangle high that base right stand is t, then: Triangle width (L) = Or L = With s = C t a B A b c Circumference (K)= a + b + c Next!

12. Adaptif Hal.: 11 ANGLE AND PLANE Width and the circumference of flat plane The formula of width in every square is: Width = side length X side length L = s x s L = s 2 Circumference (K) = 4 x side 2. Square Width

13. Adaptif Hal.: 12 ANGLE AND PLANE Width and circumference of flat plane Width Formula in every circle is: Width = π x radius x radius = π x r x r = π r 2 Circle circumference = 2 r by π = 3,14 or π = 3. Width and circumference of circle

14. Adaptif Hal.: 13 ANGLE AND PLANE Width and Circumference of flat plane 4. Width and circumference of rectangular Rectangular ABCD A p B C D Width ABCD = p x Circumference ABCD = (2 x p) + ( 2 x ) Example: Rectangular ABCD, the length is 8 cm and wide is 6 cm. Determine the width and circumference of that rectangular! Answer: Rectangular width = p x = 8 x 6 = 48 Rectangular circumference = (2 x p) + (2 x ) = (2 x 8) + ( 2 x 6) = 16 + 12 = 28

15. Adaptif Hal.: 14 ANGLE AND PLANE Width and circumference of flat shape 5. Width and circumference of parallelogram b t a Example: Parallelogram has sides a and b and tall t Parallelogram width (L)= a x t Parallelogram circumference (K)= 2 (a + b) Example: Find the width and the circumference of Parallelogram in the picture below! Answer: 7 5 4 Width = 7 cm x 4 cm = 28 cm 2 Circumference = 2 ( 7 cm + 5 cm) = 2 x 12 cm = 24 cm

16. Adaptif Hal.: 15 ANGLE AND PLANE Width and circumference of flat shape 6. Width and circumference of kites Kite ABCD D A C B Width (L)= ½ (a xb) b a Circumference= AB+BC+CD+DA Example: Find the width of kite below, if the diagonal line is AC = 10 cm and BD= 8 cm. D Answer: Width = ½ ( AC x BD) A C = ½ ( 10 cm x 8 cm ) = 40 cm 2 B

17. Adaptif Hal.: 16 ANGLE AND PLANE Width and circumference of flat plane 7. Width and circumference of Trapezium A B Width = ½ ( AB + CD). t t Circumference = AB + BC + CD + DA C D Example: Find the trapezium width in the picture! D E C 8 10 A B 15 Answer: Width = ½ ( AB + CD) CE = = = =

18. Adaptif Hal.: 17 ANGLE AND PLANE Width and circumference of flat plane 8. Area width side n arranged Side n arranged which has length = a L = a 2 x ctg Sample: Width of 6 side arranged L = ½ a a

19. Adaptif Hal.: 18 ANGLE AND PLANE Width and circumference of flat plane 9. Area width of ellipse Area width of ellipse if the axis mayor = a and axis minor = b then: L = ab a b

20. Adaptif Hal.: 19 ANGLE AND PLANE Area width in irregular plane 1. Trapesoida Rule Width = part width. Width= d. Part width ABCD = ½ (O 1 + O 2 ), and so are the other parts, then gotten part or total width as total of all parts width. See! A M K I G E C DB FHJ NL d o 1 o 2 o 3 o 4 o 5 o 6 O 7

21. Adaptif Hal.: 20 ANGLE AND PLANE Area width of irregular plane 2. Mid Ordinate Rule y 1, y 2, … shows ordinate in the middle last ordinate. y 1 =, y 2 = Part width ABCD= y 1 x d and width CDEF = y 2 x d Total part width = y 1. d + y 2. d+ y 3. d+ …. F E D C B A y y y 2 y 3 d

22. Adaptif Hal.: 21 ANGLE AND PLANE Area width of irregular plane Example of irregular plane Determine irregular plane width beside by rules: a. Trapesoida b. Mid Ordinate Answer: a. Trapesoida Rule L = 2. L =2. L = 2. 47 = 94 5 7 10 8 12 9 13 A M K I G E C DB FHJ NL 2

23. Adaptif Hal.: 22 ANGLE AND PLANE Area width of irregular plane area Next b. Mid Ordinate y 1 =, y 2 =, y 3 =, y 4 = y 5 =, y 6 = Total width = y 1.d + y 2. d+ y 3. d + y 4. d+ y 5. d+ y 6. d = 6. 2 + 8,5. 2 + 8. 2 + 10. 2+ 10,5. 2 + 6. 2 = 12 + 17 + 16 + 20 + 21 + 12 = 98

24. Adaptif Hal.: 23 ANGLE AND PLANE Thank you Keep practicing!… The end