Angle Facts Define Perpendicular Lines Two lines at

Angle Facts Define: Perpendicular Lines Two lines at right angles (90 o) 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

Vertical Horizontal Angles at a Point 90 90 360 o 2 1 360 o 4 3 360 o

Angles at a Point d c b a Angles at a point add to 360 o Angle a + b + c + d = 3600

Angles at a Point 90 90 Example: Find angle a. a 360 o 85 o 80 o Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120 o 75 o + 85 75 80 240

Angles at a Point c d a b 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 Line Angles on a straight line add to 180 o Oblique line 90 90 180 o Angles a + b = 180 o b b 70 o Angle b = 180 – 70 = 110 o a Horizontal line 35 o x Angle x = 180 – 35 = 145 o

Angle Facts f = 360 – (45+120+110) f = 360 - 275 = 85 o Now do these: 35 o a 22 o a = 180 – 35 = 145 o b = 180 – (22+90) = 68 o 110 o f 120 o 45 o b 3 g = 360 – (90+60) = 210 g = 70 60 o 116 o d c Opposite angles are equal So c = 116 o d = 180 – 116 = 64 o g g g i = 180 - 148 = 32 o 148 o e 80 o 135 o e = 360 – (135+80) = 145 o i 3 h = 180 – i = 148 . h h = 49. 3 2 h

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 180 o. (Supplementary)

Angles between Parallel Lines

Angles between Parallel Lines

Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal d h e g a c f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal a h e g c b f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal d h g a c b f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle corresponding to the marked angle. Transversal d e h g a b f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle alternate to the marked angle. Transversal d e h g a b f Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle alternate to the marked angle. Transversal d a b c e h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle interior to the marked angle. Transversal a b c h d g e Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines Name an angle interior to the marked angle. Transversal d a b c e h g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Parallel lines remain the same distance apart.

Angles between Parallel Lines d Name an angle corresponding to the marked angle. a c h e g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) f

Angles between Parallel Lines d Name an angle alternate to the marked angle. a c b e g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) f

Angles between Parallel Lines d Name an angle interior to the marked angle. c b h e g Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) f

Angles between Parallel Lines Name in order, the angles that are alternate, interior and corresponding to the marked angle. h g e f d c b Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary)

Angles between Parallel Lines Name in order, the angles that are alternate, interior and corresponding to the marked angle. c g h f d e Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) a

Angles between Parallel Lines Finding unknown angles x= y= z= z 100 o y x 60 o Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Find the unknown angles stating reasons, from the list below.

Angles between Parallel Lines Finding unknown angles x= y= z= 105 o z x 55 o Find the unknown angles stating reasons, from the list below. 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 180 o. (Supplementary) Int. s

Angles between Parallel Lines Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties. y 95 o 60 o x Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Find the unknown angles stating reasons, from the list below.

Angles between Parallel Lines x= Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties. y= z= y x 55 o 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 180 o. (Supplementary) Find the unknown angles stating reasons, from the list below.

Angles between Parallel Lines 58 o e f g h b a 70 o c d Mixing it! Vertically opposite angles are equal. Corresponding angles are equal. Alternate angles are equal. Interior angles sum to 180 o. (Supplementary) Angle sum of a triangle (180 o) Angle on a line sum to (180 o) Base angles isosceles triangle equal. Angles at a point sum to 360 o Find the unknown angles stating reasons, from the list below. There may be more than one reason.

Angle Facts Now do these: t u t = 99 o 54 o u = 81 o w v = 54 o v w = 126 o 99 o 65 o p 38 o q Corresponding angles p = 65 o 130 o x = 130 o x Alternate angles q = 38 o y = 130 o y r 77 o s Corresponding angles r = 77 o Opposite angles (with r) or Alternate angles with 77 o s = 77 o 35 o z z = 35 o + 48 o = 83 o 48 o