Parallel Lines

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# Parallel Lines - PowerPoint PPT Presentation

Parallel Lines. Transversal. Angles Between Parallel lines. Draw a pair of parallel lines with a transversal and measure the 8 angles. Parallel lines remain the same distance apart. Vertically opposite angles are equal. vert.opp. s. Corresponding angles are equal. corr. s.

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Presentation Transcript

Transversal

Angles Between Parallel lines.

Draw a pair of parallel lines with a transversal and measure the 8 angles.

Parallel lines remain the same distance apart.

Vertically opposite angles are equal.

vert.opp. s

Corresponding angles are equal.

corr. s

Transversal

Angles Between Parallel lines

Draw a pair of parallel lines with a transversal and measure the 8 angles.

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

Transversal

Angles Between Parallel lines

Draw a pair of parallel lines with a transversal and measure the 8 angles.

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

Transversal

Angles Between Parallel lines

Name an angle corresponding to the marked angle.

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

Transversal

Angles Between Parallel lines

Name an angle corresponding to the marked angle.

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

Transversal

Angles Between Parallel lines

Name an angle corresponding to the marked angle.

a

b

d

c

Parallel lines remain the same distance apart.

f

g

h

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

Transversal

Angles Between Parallel lines

Name an angle corresponding to the marked angle.

a

b

d

Parallel lines remain the same distance apart.

e

f

g

h

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

Transversal

Angles Between Parallel lines

Name an angle alternate to the marked angle.

a

b

d

Parallel lines remain the same distance apart.

e

f

g

h

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

Transversal

Angles Between Parallel lines

Name an angle alternate to the marked angle.

a

b

d

c

Parallel lines remain the same distance apart.

e

g

h

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

Transversal

Angles Between Parallel lines

Name an angle interior to the marked angle.

a

b

c

Parallel lines remain the same distance apart.

d

e

g

h

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

Transversal

Angles Between Parallel lines

Name an angle interior to the marked angle.

a

b

d

c

Parallel lines remain the same distance apart.

e

g

h

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

b

c

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

80o

Int. s

60o

vert.opp. s

120o

Int. s

Angles Between Parallel lines

Finding unknown angles

 x =

 y =

 z =

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

z

100o

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

105o

corr. s

55o

alt. s

125o

Int. s

Angles Between Parallel lines

Finding unknown angles

 x =

 y =

 z =

105o

55o

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

z

y

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

 x =

85o

Int. s

 y =

120o

Int. s

Angles Between Parallel lines

Finding unknown angles

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

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

y

95o

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

125o

Int. s

55o

Int. s

125o

Int. s

55o

125o

125o

Angles Between Parallel lines

 x =

Finding unknown angles

 y =

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

 z =

y

x

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

 a =

 b =

 c =

58o

vert.opp. s

 d =

32o

s in tri

 e =

32o

52o

58o

64o

58o

64o

isos tri

s on line

corr. s

s at a point

isos tri

alt. s

 f =

 g =

 h =

Angles Between Parallel lines

58o

b

a

c

e

g

f

d

70o

Mixing it!

h

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