![Angle Relations Comp & Supple Vertical Adjacent (Teacher) [Autosaved].pptx](https://cdn.slidesharecdn.com/ss_thumbnails/anglerelationscompsuppleverticaladjacentteacherautosaved-241209052056-6677bf45-thumbnail.jpg?width=640&height=640&fit=bounds)
angle facts.ppt angle facts angle facts angle facts
- 1. Angle Facts Objectives: F GradeExpress fractions of full turns in degrees and vice versa Recognise acute, obtuse, reflex and right angles Estimate angles and measure them accurately Use properties of angles at a point and angles on a straight line Understand the terms ‘perpendicular lines and ‘parallel lines’ D Grade Recognise corresponding angles and alternate angles
- 2. Angle Facts Define: PerpendicularLines Define: Parallel Two lines at right angles (90o) to each other Straight lines that are always the same distance apart and never meet
- 3. Angle Facts Starter: Name theseangles: Acute Reflex Right Angle Obtuse
- 4.
- 5. a b c d Angles at apoint add to 360o Angle a + b + c + d = 3600 Angles at a Point
- 6. 75o 85o 80o a Example: Find anglea. 90 90 90 90 360o Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120o 85 75 80 + 240 Angles at a Point
- 7. a b c d Opposite Angles areequal Angle a + b = 1800 because they form a straight line Angle c + d = 1800 because they form a straight line Angle c + b = 1800 because they form a straight line Angle d + a = 1800 because they form a straight line So a = c and b = d Angles at a Point
- 8. Horizontal line Oblique line a b Anglesa + b = 180o 70o b Angle b = 180 – 70 = 110o x 35o Angle x = 180 – 35 = 145o 90 90 Angles on a straight line add to 180o 180o Angles on a Line
- 9. Angle Facts Now dothese: f g g g 2h h 60o 45o 120o 110o 35o a b 22o 116o c d e 135o 80o 148o i a = 180 – 35 = 145o b = 180 – (22+90) = 68o Opposite angles are equal So c = 116o d = 180 – 116 = 64o e = 360 – (135+80) = 145o f = 360 – (45+120+110) f = 360 - 275 = 85o 3g = 360 – (90+60) = 210 g = 70 i = 180 - 148 = 32o 3h = 180 – i = 148 h = 49.3 .
- 10. Parallel lines remain thesame distance apart. Transversal Draw a pair of parallel lines with a transversal and measure the 8 angles. Vertically opposite angles are equal. Corresponding angles are equal. Angles between Parallel Lines
- 11. Parallel lines remain thesame distance apart. Transversal Draw a pair of parallel lines with a transversal and measure the 8 angles. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Angles between Parallel Lines
- 12. Parallel lines remain thesame distance apart. Transversal Draw a pair of parallel lines with a transversal and measure the 8 angles. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 13.
- 14.
- 15. Parallel lines remain thesame distance apart. Transversal Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) a d c e g h f Name an angle corresponding to the marked angle. Angles between Parallel Lines
- 16. Parallel lines remain thesame distance apart. Transversal a b c e g h f Name an angle corresponding to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 17. Parallel lines remain thesame distance apart. Transversal a b c h g d f Name an angle corresponding to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 18. Parallel lines remain thesame distance apart. Transversal a b e h g d f Name an angle corresponding to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 19. Parallel lines remain thesame distance apart. Transversal a b e h g d f Name an angle alternate to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 20. Parallel lines remain thesame distance apart. Transversal a b e h g d c Name an angle alternate to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 21. Parallel lines remain thesame distance apart. Transversal a b e h g d c Name an angle interior to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 22. Parallel lines remain thesame distance apart. Transversal a b e h g d c Name an angle interior to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 23. a f e h g d c Name an angle correspondingto the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 24. a f e b g d c Name anangle alternate to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 25. h f e b g d c Name anangle interior to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 26. h f e b g d c Name in order,the angles that are alternate, interior and corresponding to the marked angle. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angles between Parallel Lines
- 27. a f e h g d c Vertically opposite anglesare equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Name in order, the angles that are alternate, interior and corresponding to the marked angle. Angles between Parallel Lines
- 28. x Vertically opposite anglesare equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Finding unknown angles 100o Find the unknown angles stating reasons, from the list below. y z 60o x = y = z = 80o Int. s 60o vert.opp. s 120o Int. s Angles between Parallel Lines
- 29. x Vertically opposite anglesare equal. vert.opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180o .(Supplementary) Int. s Finding unknown angles 105o Find the unknown angles stating reasons, from the list below. y z x = y = z = 105o corr. s 55o alt. s 125o Int. s 55o Angles between Parallel Lines
- 30. x Vertically opposite anglesare equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Finding unknown angles 95o Find the unknown angles stating reasons, from the list below. y x = y = 85o Int. s 120o Int. s 60o Unknown angles in quadrilaterals and other figures can be found using these properties. Angles between Parallel Lines
- 31. x Vertically opposite anglesare equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Finding unknown angles Find the unknown angles stating reasons, from the list below. y 55o z x = y = z = What does this tell you about parallelograms? 125o Int. s 125o 55o Int. s 55o 125o Int. s 125o Unknown angles in quadrilaterals and other figures can be found using these properties. Angles between Parallel Lines
- 32. 70o a Vertically opposite anglesare equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Find the unknown angles stating reasons, from the list below. There may be more than one reason. 58o vert.opp. s 32o s in tri 58o 32o alt. s b d c Angle sum of a triangle (180o) Angle on a line sum to (180o) 58o s on line e 58o corr. s 52o s at a point f g h Base angles isosceles triangle equal. 64o isos tri a = b = c = d = e = f = g = h = 64o isos tri Angles at a point sum to 360o Mixing it! Angles between Parallel Lines
- 33. Angle Facts Now dothese: 65o p 99o 77o 38o 54o 48o 35o z 130o y x w t u s r q v Corresponding angles p = 65o Alternate angles q = 38o Corresponding angles r = 77o Opposite angles (with r) or Alternate angles with 77o s = 77o t = 99o v = 54o u = 81o w = 126o x = 130o y = 130o z = 35o + 48o = 83o