Angle Facts Define: Perpendicular Lines Two lines at right angles (90o) to each other Define: Parallel Straight lines that are always the same distance apart and never meet
Angle Facts Starter: Name these angles: Acute Obtuse Right Angle Reflex
Angles at a Point 1 2 360o 360o 360o 3 4 360o 360o Vertical Horizontal 90 Vertical Horizontal 1 2 360o 360o 360o 3 4 360o 360o
Angles at a point add to 360o b c d Angles at a point add to 360o Angle a + b + c + d = 3600
Angles at a Point Example: Find angle a. a 75o 85o 360o 80o + 90 360o 75o 85o 80o a Example: Find angle a. 85 75 80 + 240 Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120o
Opposite Angles are equal Angles at a Point a b c d Opposite Angles are equal 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 on a straight line add to 180o Angles on a Line 90 Angles on a straight line add to 180o 180o Oblique line Horizontal line a b Angles a + b = 180o 70o b x 35o Angle b = 180 – 70 = 110o Angle x = 180 – 35 = 145o
Angle Facts Now do these: . f = 360 – (45+120+110) f = 360 - 275 = 85o b 22o 116o c d e 135o 80o 148o i a = 180 – 35 = 145o b = 180 – (22+90) = 68o 3g = 360 – (90+60) = 210 g = 70 Opposite angles are equal So c = 116o d = 180 – 116 = 64o i = 180 - 148 = 32o 3h = 180 – i = 148 e = 360 – (135+80) = 145o h = 49.3 .
Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal.
Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal.
Angles between Parallel Lines Draw a pair of parallel lines with a transversal and measure the 8 angles. Transversal Parallel lines remain the same distance apart. Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines
Angles between Parallel Lines
Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal a d c Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal a b c Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal a b d c Parallel lines remain the same distance apart. f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal a b d Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle alternate to the marked angle. Transversal a b d Parallel lines remain the same distance apart. e f h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle alternate to the marked angle. Transversal a b d c Parallel lines remain the same distance apart. e h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle interior to the marked angle. Transversal a b c Parallel lines remain the same distance apart. d e h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name an angle interior to the marked angle. Transversal a b d c Parallel lines remain the same distance apart. e h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines d a h e c g 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 d a e c b g 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 d h e c b g f 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 Name in order, the angles that are alternate, interior and corresponding to the marked angle. e h f g d c b Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Name in order, the angles that are alternate, interior and corresponding to the marked angle. d a c h e g f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Finding unknown angles x = 80o Int. s y = 60o vert.opp. s z = 120o Int. s z 100o Find the unknown angles stating reasons, from the list below. y x 60o Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Finding unknown angles x = 105o corr. s y = 55o alt. s z = 125o Int. s 105o z 55o Find the unknown angles stating reasons, from the list below. x y Vertically opposite angles are equal. vert.opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180o .(Supplementary) Int. s
Angles between Parallel Lines Finding unknown angles x = y = 85o Int. s Unknown angles in quadrilaterals and other figures can be found using these properties. 120o Int. s y 95o Find the unknown angles stating reasons, from the list below. 60o x Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines Finding unknown angles 125o Int. s x = 55o Int. s y = Unknown angles in quadrilaterals and other figures can be found using these properties. 125o Int. s z = x y Find the unknown angles stating reasons, from the list below. 55o z What does this tell you about parallelograms? Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary)
Angles between Parallel Lines c = d = e = f = g = h = 58o vert.opp. s 32o s in tri 58o a b 32o alt. s 58o s on line 58o corr. s e c g f d 52o s at a point 70o 64o isos tri h Mixing it! 64o isos tri Vertically opposite angles are equal. Find the unknown angles stating reasons, from the list below. There may be more than one reason. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180o .(Supplementary) Angle sum of a triangle (180o) Angle on a line sum to (180o) Base angles isosceles triangle equal. Angles at a point sum to 360o
Angle Facts Now do these: 65o p 99o 77o 38o 54o 48o 35o z 130o y x w t u s r q v t = 99o u = 81o v = 54o w = 126o Corresponding angles p = 65o x = 130o Alternate angles q = 38o y = 130o Corresponding angles r = 77o Opposite angles (with r) or Alternate angles with 77o s = 77o z = 35o + 48o = 83o