PPT_Kompan rebolusyunaryo group 4. Rebulusyunaryo ng wikang filipino

Report

1. Grade 10 Mathematics Quarter II Week 3

2. CLASSPOINT CODE: Checking of Attendance

3. PRAYER LEADER MARINEL KYLA GALUT

4. Most Essential Learning Competency Derives inductively the relations among chords, arcs, central angles, and inscribed angles . (M10GE – IIc-1 )

5. 1. Define a circle and describe other terms related to circle and derive their relationships. Objectives: 2. Identify the central angles and intercepted arcs of a given circle. 3. Find the measure of the central angles and intercepted arcs of a given circle.

6. GUIDE QUESTIONS 1. What is a circle? 2. What are the auxiliary parts of a circle? 3. How are these parts related? 4. What are central angles and intercepted arcs? 5. How are central angles and their intercepted arcs related?

7. A circle is a set of all points with the same distance from a fixed point called the center. The center is used to name a circle

8. ● O ʘ O

9. Radius ● O ● A   And all radii on the same circle are congruent.

10. OA = 5 units OB = 5 units OC = 5 units ● O ● A B ● ● C

11. ● O ● A B ● Chord   Chord a line segment having endpoints on the circle

12. ● ● F E ● D ● ● C ● A B ●     Chords O

13. ● ● F E ●   Chord Diameter Longest chord Twice the radius Diameter

14. ● ●   O Secant A line, segment or ray that intersects a circle at exactly two points D ● C

15. ● Secants ● H ● G     ● O Y X ●

16. ● A ● I ● J ● N R . M . W . ● O Tangent Tangent a line, segment or a ray that intersects a circle at exactly one point

17. ● A ● E ● X ● C ● L ● Y Which of the following is NOT a radii? A.   B.   C.   D.  

18. ● E ● X ● C ● L ● Y ● A 2. Which of the following is NOT a chord? A.   B.   C.   D.  

19. ● E ● X ● C ● L ● Y ● A 3. Which of the following is a diameter? A.   B.   C.   D.  

20. ● E ● X ● C ● L ● Y 4. Which is a secant line ● A A.   B.   C.   D.  

21. ● E ● X ● C ● L ● Y ● A 5. Name a tangent line. A.   B.   C.   D.  

22. ● A X ● C Arc is a part of a circle between any two points. It is measured in terms of degrees. minor semicircle major Symbol ●

23. A semicircle is an arc which is one-half of a circle. It measures exactly 180 . 180

24. A minor arc is less than a semicircle and its measure is between 0 and 180 0.

25. A major arc is greater than a semicircle which measures between 180 and 360 0.

26. ● A ● X ● Y Semicircle XEY ● C ● E Semicircle XCY X Y

27. ● A ● X ● Y EX ● C ● E X Y CY EY Minor Arcs EX, EY, CY

28. ● A ● ● CEY C ● E Semicircles: XEY and XCY minor arcs: EX, CY, and EY major arcs: CEY and EYX Y Major Arc

29. A central angle of a circle is an angle formed by two radii and its vertex is the center of the circle.

30. ● Y ● A Referring to ʘ A X EAX   E ● ● EAY   Central angles.

31. An intercepted arc is created when lines or subsets of a line cuts across a section of the circumference of a circle.

32. ● ● C Y ● A EC is a minor arc intercepted by inscribed angle EYC. E ●

33. ● Y ● EX is a minor arc intercepted by central angle EAX and also intercepted by inscribed angle EYX. ● E X ● A

34. The sum of the measures of the central angles of a circle with no common interior points is 360 . 360

35. In the figure, angles 1, 2, 3, and 4 are examples of central angles without common interior points. 1 3 2 4 Thus, m + m + m + m = 360  

36. G F C Central FCG intercepts minor arc FG  

37. E I C Central angle ECI intercepts minor arc EI

38. A G B C Central angle ACG intercepts major arc GBA

39. A C Minor arc AI is intercepted by central angle ACI I

40. C D F H Major arc FDH is intercepted by central angle FCH

41. Arc Addition Postulates The measure of an arc formed by two adjacent non-overlapping arcs (arc that share exactly one point) is equal to the sum of the measures of these two arcs.

42. Using circle D, mAC = mAB + mBC mAC = 60 + 90 mAC = 150 90 B A C D 60 H

43. ACTIVITY Determine the measures of the given arcs and angles.

44. N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 45 30 Q m or m Answer: The measure of is 45 .   45 A. 30 B. 75 C . 45 D. 15

45. N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 2. Measure of arc LM Answer: The measure of arc LM is 45 because the measure of that intercepts arc LM is 45 .   N M Y L X Z O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 45 30 Q 45 A. 75 B. 45 C . 30 D. 15

46. N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 3. Measure of arc XQ Answer: Arc XQ is 30 . and are vertical angles and a pair of vertical angles are congruent. It follows that their intercepted arcs also are congruent.   N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 45 30 Q 45 A. 75 B. 45 C . 30 D. 15

47. : Defined Circle Described terms related to circle Derived their relationships Identified and measured the central angles and intercepted arcs of a circle

48. D 1. The angle intercepting arc GA. A E G F B H I C Answer:  

49. D 2. The angle intercepting arc DH. A E G F B H I C Answer:  

50. D 3. The arc intercepted by ACH   A E G F B H I C Answer: AH

51. N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 1. Measure of Answer: 15   N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5

52. N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 2. Measure of arc PO Answer: 45 N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5

53. N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 3. Measure of Answer: 45   N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y G X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5 N M Y L X Z P O C 15 R 8 1 2 7 6 5 4 3 4 5 30 Q 4 5

54. “Life is a circle. The end of one journey is the beginning of the next” -Anonymous

55. References: Books Callanta, Melvin M., et al. 2015. Mathematics Learner’s Module Philippines. Department of Education. B. Government Publications ADM Mathematics 10 Module 19: The Relations among Chords, Arcs, Central Angles and Inscribed Angles. Department of Education. C. Online and Other Sources freepik.com p ngtree. com