mathematics GRADE 10 second quarter.pptx

math 10

1. The Circle of Life MATHEMATICS 10

2. 2 j Prayer Dear Lord and Father of all, Thank you for today. Thank you for ways in which you provide for us all. For Your protection and love we thank you. Help us to focus our hearts and minds now on what we are about to learn. Inspire us by Your Holy Spirit as we listen and write. Guide us by your eternal light as we discover more about the world around us. We ask all this in the name of Jesus. Amen.?

3. 3

4. 4 CHECKING OF ATTENDANCE

5. Objectives 1. Recall the theorems on circles 5 2. Solve problems involving circles

6. Riddle # 1 I have many shapes. I look square from outside, circle when opened and triangle when taken out. What Am I? 6

7. I only have a head and a tail but don’t have a body. What Am I? Riddle #2 7

8. I am not a ball but yet a sphere, & holds all lands & people year after year What Am I? Riddle # 3 8

9. I have a face but no eyes, have hands but no arms nor legs What Am I? Riddle # 4 9

10. 10 1 2 3 4 5 6 7 8 WHAT’S MY SIZE

11. 1 V S I In circle S below, how big is angle VSI if the measure of arc VI is 140° 140°

12. 2 In the figure below, the measure of arc XY is 150° and arc MN is 30°. How big is angle XPY? P N M X Y 60°

13. 3 In the circle below, how big is angle SAY if arc DSY is a semi circle and the measure of angle SAD is 70°. S A D Y 110°

14. 4 Quadrilateral SML is inscribed in circle E. If the measure of angle SMI is 78° and MSL is 95°, how big is angle MIL? M I S L E 78° 95° 85°

15. 5 In circle M below, how big is angle BRO if angle BMO measures 60° R B O M 30°

16. 6 What is the measure of minor arc AB? C B A M 20 ° 192° 64°

17. 7 In the figure below, SY and EY are secants. If SY = 15 cm, TY=6 cm, and LY =8 cm. How long is segment EY? S T Y E L 11.25 cm

18. 8 In the figure, segment JE and segment AN intersect each other. How long is ON if OA is 4 cm, JO is 6 cm and OE is 8 cm? 12 cm J A N E O

19. 19 Two straight pipes intersect under a circluar garden and intercept non adjacent arcs that measure 38 and 40 degrees. What is the measure of the obtuse vertical angles formed where two pipes intersect?

20. 20 U nderstanding the problem Unknown The measure of the obtuse vertical angles formed by the two intersecting pipes

21. 21 U nderstanding the problem Given Non adjacent arcs measuring 38 and 40 3 8 4

22. 22 2. D evise a plan (translate) Concept of intercepted arcs and angles that form a linear pair m∠DBE =1/2 (m DE+m AC) m∠ABD + m∠DBE=180 ° 38° 40° A B C D E

23. 23 m∠DBE =1/2 (m DE+m AC) m∠DBE =1/2 (40 ° +38 ° ) m∠DBE =1/2 (78 ° ) m∠DBE =39 ° 3. C arry out the plan (solve). m∠ABD + m∠DBE=180 ° m∠ABD + 39 ° =180 ° m∠ABD =180 ° - 39 ° m∠ABD = 141 °

24. 24 4. L ook back (check and interpret) 38° 40° A B C D E 39° 39° 141°

25. 25 Rodeleine baked a circular hawaiian pizza for her 7 friends which will be served as their snack while reviewing for their upcoming Quiz in Mathematics. The pizza diameter is 16 inches. If the pizza is to be cut into equal slices, what is the measure of the angle formed by a slice of the pizza?

26. 26 Solution Slice of pizza = total measure of whole pizza number of parts = 360 ° 8 = 45 °

27. 27 Mang Karyo sells sorbetes in a cone that forms an arc of 250 degrees, ID and ED are tangents to the circle as shown. What is the measure of the angle formed at the bottom of the cone?

28. 28 Given ICE = 250° IE = 360° - 250° IE = 110° I C E D  

29. 29 Steps in Solving Problems 1. U nderstand the problem 2. D evise a plan (translate). 3. C arry out the plan (solve). 4. L ook back (check and interpret)

30. 30 Selena, Joy and Charito are practicing their skills in throwin darts. They throw three darts S, J, and C respectively hit the outer edge of the dart board. The 4th dart thrown by Joy (L) landed on the wall. How far is it from the dart thrown by Selena (S) when LJ is 9 inches and JC is 16 inches?

31. 31 Josielyn cooked puto(steamed rice muffin) for her friends. She cut it into rectangular peices so that everyone can have their share. She separates the portion with the most number of pieces represented by angle UJT. If the measure of arc UT is 110 degrees and the measure of arc PO is 50 degrees, what is thof angle UJT?

32. 32 Given LJ = 9 in JC = 16 in c c c   L J S C

33. 33 T P J O U Given UT = 110° PO =50°  

34. 34 Matt, Joey, and Romy ar standing in front of the gate of Echague National High School. They stand in different position away from following health protocols. Their position forms an arc of a circle. If the viewing angle of Joey is 72°, what are the measures of the viewing angles of Matt and Romy?

35. 35 SOLUTION Let x and y be the ends of the gate. The viewing angles of Matt and Romy intercept the same arc with the viewing angle of Joey. Answer is 72 ° X Y Romy Joey Matt 72°

36. Watch Me Later! 36 https://www.youtube.com/watch?v=dtyJ2esB-X8&t=54s