Parallel Lines.

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Presentation transcript:

Parallel Lines

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. vert.opp. s Corresponding angles are equal. corr. s

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. vert.opp. s Corresponding angles are equal. corr. s Alternate angles are equal. alt. s

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. 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

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. 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 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. 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 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. 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 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. 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 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. 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 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. 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 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. 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 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. 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 d a h e c g f Name an angle corresponding to the marked angle. 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 d a e c b g f Name an angle alternate to the marked angle. 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 d h e c b g f Name an angle interior to the marked angle. 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 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. 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 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. 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 = 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. 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 = 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. 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 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. 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  c =  d =  e =  f =  g =  h = 58o vert.opp. s 32o s in tri 58o 32o alt. s a b 58o s on line e c 58o corr. s g f d 52o s at a point 70o 64o isos tri h Mixing it! 64o isos tri Vertically opposite angles are equal. vert.opp. s Find the unknown angles stating reasons, from the list below. There may be more than one reason. Corresponding angles are equal. corr. s Alternate angles are equal. alt. s Interior angles sum to 180o .(Supplementary) Int. s Angle sum of a triangle (180o) s in tri Angle on a line sum to (180o) s on line Base angles isosceles triangle equal. isos tri. Angles at a point sum to 360o s at point