TRIANGLE INEQUALITY THEOREMS _ FOR OBSERVATION.pptx

This lesson discussed about triangle inequality theorems. It tackles how to find the range of the length of the sides of triangle.

1. Mathematics may not teach us how to add happiness or how to minus sadness. But it teach us one important thing. Every problem has a solution. Good Morning!

2. Let’s Investigate!

3. 1 2 3 6 5 4 Find the 3 interior angles, and the 3 exterior angles with their corresponding remote interior angles.

4. 1 2 3 6 5 4 Find the 3 interior angles.  

5. 1 2 3 6 5 4 Find the 3 exterior angles. 7  

6. 1 2 3 6 5 4 Find the remote interior angles of .   2  

7. 1 2 3 6 5 4 Find the remote interior angles of    

8. 1 2 3 6 5 4 Find the remote interior angles of    

9. The object of hangman is to guess the secret word before the TRIANGLE is hung . Players take turns selecting letters to narrow the word down. Players can take turns or work together. Gameplay continues until the players guess the word or they run out of guesses and the stick figure is hung.

10. T R I A N G L E A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ? ? ? Thank you ! Click here T R I A N G L E You Failed! Try Again

11. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I N E Q U A L I T ? ? ? Thank you ! Click here Y I N E Q U A L I T Y You Failed! Try Again

12. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z H T E O R E M ? ? ? Thank you ! Click here S H T E O R E M S You Failed! Try again

13. TRIANGLE INEQUALITY THEOREMS

14. First Two Sides Third Side a c b a a b b c c A B C b c a 6 11 9 9 9 9 6 6 6 11 11 11 20 15 17 Sum 6 11 9      

15.       Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

16. Triangle Inequality Theorem a=5 b=7 c=10   5 10   b   5 7   7     12 10   15   17  

17. Question: Can any three length of segments form a triangle?

18. Let’s Investigate Again!

19. Example : Which length/s can form a triangle? A.) 5, 7, 12 B.) 4, 8, 15 C.) 6, 10, 9

20. Given lengths 𝑎 = 5 , 𝑏 = 7, 𝑐 = 12 Decision - Not a Triangle 𝑎 + 𝑏 > 𝑐 𝑎 + 𝑐 > 𝑏 𝑏 + 𝑐 > 𝑎 5 + 7 > 12 False 5 + 12 > 7 True 7 + 12 > 5 True

21. 8 + 15 > 4 True Given lengths 𝑎 = 4, 𝑏 = 8, 𝑐 = 15 Decision Not a Triangle 𝑎 + 𝑏 > 𝑐 4 + 8 > 15 False 𝑎 + 𝑐 > 𝑏 4 + 15 > 8 True 𝑏 + 𝑐 > 𝑎

22. 𝑎 + 𝑏 > 𝑐 Decision Triangle 𝑏 + 𝑐 > 𝑎 10 + 9 > 6 True 𝑎 + 𝑐 > 𝑏 6 + 9 > 10 True Given lengths 𝑎 = 6, 𝑏 = 10, 𝑐 = 9 6 + 10 > 9 True

23.       Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

24. Example 2. Two sides of a triangle measures 15cm and 9cm. Write an inequality that represents the range of values for possible length of the third side.

25. 15cm 9cm ?

26. Let c an unknown side of a triangle. To find the range of possible measure of side c, the inequality below may be used: (a- b) < c < (a + b) Difference < c < Sum

27. (a - b) < c < (a + b) Given : a =15 b =9 c =? 15 - 9 < c < 15 + 9 6 < c < 24 The value of c will range from 7 - 23

28. 15 + 9 > 7 24 > 7 Correct 15 + 7 > 9 22 > 9 Correct 9 + 7 > 15 16 > 15 Correct

29. 15 + 9 > 6 24 > 6 Correct 15 + 6 > 9 21 > 9 Correct 9 + 6 > 15 15 > 15 False

30. 15 + 9 > 23 15 + 23 > 9 24 > 23 Correct 38 > 9 Correct 9 + 23 > 15 32 > 15 Correct

31. 15 + 9 > 24 15 + 24 > 9 24 > 24 False 39 > 9 Correct 9 + 24 > 15 33 > 15 Correct

32. It’s time to engage!

33. Which of the following could be the lengths of the sides of a triangle. Write YES or NO. 12, 11, 10 2, 3, 4 3, 2, 1 7, 13, 7 13, 12, 5 YES YES NO YES YES

34. 15m 15m A carpenter is building a house, he used 15m woods for the legs of the A-Frame. What should be the range of the length of wood for the base? ?

35. (a - b) < c < (a + b) Given : a =15 b = 15 c =? 15 - 15 < c < 15 + 15 0 < c < 30 The length of the wood for the base will range from 1 – 29 meters.

36. FACTORING POLYNOMIALS

37. Direction: Read each question carefully and choose the letter that corresponds to the correct answer. Write your answer in your answer sheet.

38. 1. Which of the following combinations could be three sides of a triangle? A. 5, 6, 11 B. 1, 3, 5 C. 7, 7, 14 D. 5, 16, 20 D. 5, 16, 20

39. 2. Two sides of a triangle are 15 and 8. Which of the following cannot be the third side? A.   B.   C. 21 D.   B.  

40. 3. Suppose two sides of a triangle both measures 4 units, which can be the possible measure of the third side? Choose all the possible whole numbers. 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7

41. 4. Two sides of the triangle are 13 and 51. What is the range of the length of the 3rd side? A. 13< 3rd side <51 B. 13> 3 rd side > 51 C. 38<3rd side<64 D. 3 rd side <64 C. 38<3rd side<64

42. 5. Two legs of a triangle are 7.3 and 17.2 respectively. Given that the length of the third side is an integer, what is the largest possible length for the third side. A. 24 B. 18 C. 22 D. 20 A. 24