ANGLE BISECTOR FOR GRADE EIGHT HIGH.pptx

angle bisector

1. GUESS THE WORD PICTURE EDITION

2. ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ R I G T H T R I A N G L E NUMBER 1

3. ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ P E R P E N D I C U L A R NUMBER 2

4. ___ ___ ___ ___ ___ ___ ___ ___ T R I A N G L E NUMBER 3

5. ___ ___ ___ ___ ___ ___ ___ ___ ___ C O N G R U E N T NUMBER 4

6. ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ R I G T H A N G L E S NUMBER 5

7. ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ A N G L E B I S E C T O R NUMBER 6

8. APPLYING TRIANGLE CONGRUENCE to CONSTRUCT ANGLE BISECTOR

9. What is Angle Bisector? - a line or ray that divides an angle into two congruent angles .

10. How to Construct Angle Bisector of a Triangle Given: any ∠ABC To construct: ____ bisector of ∠ABC D __ __ BD Before After

11. Angle Bisector of a Triangle - AD is the angle bisector of _____. ∠BAC - Name the two congruent angles. ∠BAD ≅ ∠CAD - Name the two congruent right angles. ∠ BDA ≅ ∠CDA

12. Angle Bisector of a Triangle - ____ is the angle bisector of ∠ LMN . MO - Name the two congruent angles. ∠LMO ≅ ∠NMO - Name the two congruent right angles. ∠LOM ≅ ∠NOM

13. PROBLEM 1: 1. In ∆LMN, ∠1 ≅ ∠2. If m∠1 = 53°, what is m∠2? ∠1 ≅ ∠ 2 53 ° ≅ ? 53 ° ≅ 53 °

14. PROBLEM 2: 2. In ∆LMN, segment MO is angle bisector of ∠LMN. If m ∠LMO is 40° and m ∠NMO is 4x, find the value of x and m ∠NMO . ∠ 1 ≅ ∠ 2 40 = 4x = 10 ° = x   ∠NMO = 4x ∠ NMO = 4(10) ∠ NMO = 40 °

15. PROBLEM 3: 2. In ∆LMN, segment MO is angle bisector of ∠LMN. If m ∠LMO is 40° and m ∠NMO is 65, find the value of 5x and m ∠NMO . ∠ 1 ≅ ∠ 2 65 ° = 5 x = 13 ° = x   ∠NMO = 5x ∠ NMO = 5(13) ∠ NMO = 65 ° 65 ° 5 x

16. 4. In ∆DEF , ∠1 ≅ ∠2 . If m∠1 = 2x − 55 and m∠2 = x + 5 , what is the value of x and m∠1, m∠2 and m∠DEF ? PROBLEM 4: ∠1 ≅ ∠ 2 2x − 55 = x + 5 2x − x = 5 + 55 x = 60 m∠1 = 2x − 55 m ∠ 1 = 2(60) – 55 m∠ 1 = 120 – 55 m∠ 1 = 65 ° m∠2 = x + 5 m∠ 2 = x + 5 m∠ 2 = 65 ° m ∠ DEF = m∠ 1 + m∠ 2 m∠DEF = 65 ° + 65 ° m∠DEF = 130 °

17. Test yourself!

18. Given: AS is an angle bisector of ∠CAN. ∠1 = 50 ° and ∠2 = (3x + 5) ° Find x: ∠1 ≅ ∠2 50 = (3x + 5 )° -3x = 5 – 50 = x = 15   Find m∠ 2: m∠ 2 = (3x + 5) ° m∠2 = 3(15) + 5 m∠ 2 = 45 + 5 m∠ 2 = 50 ° Find m ∠ 3 : 180° = m∠1+ m∠2+m∠3 180° = 50° + 90° + m ∠3 -m∠ 3 = 50° + 90° - 180° - m∠ 3 = 140 ° – 180 ° m∠ 3 = 40 ° Find m ∠ 4 : m ∠ 4 = m∠3 m∠ 4 = 40°

19. QUIZ

20. perpendicular bisector C. angle bisector definition of bisector D. triangle bisector 1. It is a line or ray that divides an angle into two congruent angles .

21. a 90° C . 20° 60° D . 40° 2. If a 120 angle is bisected, what will be the degree measure of each angles?  

22. 3. What is the two congruent angles? ∠XYZ ≅ ∠WZX ∠ZXY ≅ ∠WXY ∠YXZ ≅ ∠YXW ∠WXZ ≅ ∠YXZ

23. 4 . In m ∠WXY , if the m ∠1 = 40, what is the measure of m ∠2? 40 ° C . 80° 20 ° D . 90°

24. a 5 . Find PQ 56 28 14 26

25. perpendicular bisector C. angle bisector definition of bisector D. triangle bisector 1. It is a line or ray that divides an angle into two congruent angles .

26. perpendicular bisector C. angle bisector definition of bisector D. triangle bisector 1. It is a line or ray that divides an angle into two congruent angles .

27. a 90° C . 20° 60° D . 40° 2. If a 120 angle is bisected, what will be the degree measure of each angles?  

28. a 90° C . 20° 60° D . 40° 2. If a 120 angle is bisected, what will be the degree measure of each angles?  

29. 3. What is the two congruent angles? ∠XYZ ≅ ∠WZX ∠ZXY ≅ ∠WXY ∠YXZ ≅ ∠YXW ∠WXZ ≅ ∠YXZ

30. 3. What is the two congruent angles? ∠XYZ ≅ ∠WZX ∠ZXY ≅ ∠WXY ∠YXZ ≅ ∠YXW ∠WXZ ≅ ∠YXZ

31. 4 . In m ∠WXY , if the m ∠1 = 40, what is the measure of m ∠2? 40 ° C . 80° 20 ° D . 90°

32. 4 . In m ∠WXY , if the m ∠1 = 40, what is the measure of m ∠2? 40 ° C . 80° 20 ° D . 90°

33. a 5 . Find PQ 56 28 14 26

34. a 5 . Find PQ 56 28 14 26