3angles (between Parallels).ppt 3ze63

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 d

h

e

g

a

c

f

Vertically opposite angles are equal.

* Alternate angles are equal.

Corresponding angles are equal. Interior angles sum to 180o .(Supplementary)

Parallel lines remain the same distance apart.

vert.opp. s corr. s alt. s Int. s

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.

* Alternate angles are equal.

Corresponding angles are equal. Interior angles sum to 180o .(Supplementary)

Parallel lines remain the same distance apart.

vert.opp. s corr. s alt. s Int. s

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.

* Alternate angles are equal.

Corresponding angles are equal. Interior angles sum to 180o .(Supplementary)

Parallel lines remain the same distance apart.

vert.opp. s corr. s alt. s Int. s

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.

* Alternate angles are equal.

Corresponding angles are equal. Interior angles sum to 180o .(Supplementary)

Parallel lines remain the same distance apart.

vert.opp. s corr. s alt. s Int. s

Angles Between Parallel lines Name an angle alternate to the marked angle.

Transversal d

e h

g

a

b

f

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 180

o

.(Supplementary)

Int. s

Angles Between Parallel lines Name an angle alternate to the marked angle.

Transversal d

a

b c

e h

Parallel lines remain the same distance apart.

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 180

o

.(Supplementary)

Int. s

Angles Between Parallel lines Name an angle interior to the marked angle.

Transversal a

b c

h

*

d

g

e

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 Name an angle interior to the marked angle.

Transversal d

a

b c

e h

*

Parallel lines remain the same distance apart.

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 Name an angle corresponding to the marked angle.

*

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

d Name an angle alternate to the marked angle.

*

a c

b

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

d Name an angle interior to the marked angle.

*

c

b

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 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.

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.

c

g

h f

d

a

e

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

z

x=

80o

Int. s

y=

60o

vert.opp. s

z=

120o

Find the unknown angles stating reasons, from the list below.

100o

y

Int. s

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

105

105o

y=

55o

alt. s

z=

125o

Int. s

o

x=

z x

55o

corr. s

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 180o .(Supplementary)

Int. s

Angles Between Parallel lines Finding unknown angles Unknown angles in quadrilaterals and other figures can be found using these properties.

y

x=

85o

Int. s

y=

120o

Int. s

Find the unknown angles stating reasons, from the list below.

95o

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 Unknown angles in quadrilaterals and other figures can be found using these properties.

125o

Int. s

y=

55o

Int. s

z=

125o

Int. s

55o y

x o 125 55o

x=

125zo

What does this tell you about parallelograms?

Find the unknown angles stating reasons, from the list below.

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 58

o

e f

g h

b

a

70o

c d

Mixing it!

a=

58o

vert.opp. s

b=

32o

s in tri

c=

32o

alt. s

d=

58o

s on line

e=

58o

corr. s

f =

52o

s at a point

g=

64o

isos tri

h =

64o

isos tri

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

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

Find the unknown angles stating reasons, from the list below. There may be more than one reason.