Angle Facts Angle Facts es: rade Express fractions of full turns in degrees and vice versa Recognise acute, obtuse, reflex and right an Estimate angles and measure them accurately Use properties of angles at a point and angl on a straight line Understand the terms ‘perpendicular line ‘parallel lines’ D Grade Recognise corresponding angles and alternate angles
Angle Facts
Jan 05, 2016
Angle Facts. Objectives: F GradeExpress fractions of full turns in degrees and vice versa Recognise acute, obtuse, reflex and right angles Estimate angles and measure them accurately Use properties of angles at a point and angles on a straight line - PowerPoint PPT Presentation
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Angle FactsAngle Facts
Objectives:F Grade Express fractions of full turns in degrees
and vice versaRecognise acute, obtuse, reflex and right anglesEstimate angles and measure them accuratelyUse properties of angles at a point and angles
on a straight lineUnderstand the terms ‘perpendicular lines and
‘parallel lines’
D Grade Recognise corresponding angles and alternate angles
Angle FactsAngle Facts
Define: Perpendicular Lines
Define: Parallel
Two lines at right angles (90o) to each other
Straight lines that are always the same distance apart and never meet
Angle FactsAngle Facts
Starter:Name these angles:
Acute
Reflex
Right Angle
Obtuse
9090
9090
Vertical
Horizontal
360o
1
360o
2
360o
3
360o
4
360o
Angles at a PointAngles at a Point
ab
c
d
Angles at a point add to 360o
Angle a + b + c + d = 3600
Angles at a PointAngles at a Point
75o
85o 80
o
a
Example: Find angle a.90 909090
360o
Angle a = 360 - (85 + 75 + 80)
= 360 - 240 = 120o
857580+
240
Angles at a PointAngles at a Point
a
bc
d
Opposite Angles are equalAngle 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 at a PointAngles at a Point
Horizontal line
Oblique line
a b
Angles a + b = 180o
70o b
Angle b = 180 – 70 = 110o
x 35o
Angle x = 180 – 35 = 145o
90 90
Angles on a straight line add to 180o
180o
Angles on a LineAngles on a Line
Angle FactsAngle Facts
Now do these:
f
gg
g
2h
h
60o
45o 120o
110o
35oa
b
22o
116o
cd
e
135o
80o
148o
i
a = 180 – 35 = 145o
b = 180 – (22+90) = 68o
Opposite angles are equalSo c = 116o
d = 180 – 116 = 64o
e = 360 – (135+80) = 145o
f = 360 – (45+120+110)
f = 360 - 275 = 85o
3g = 360 – (90+60) = 210
g = 70
i = 180 - 148 = 32o
3h = 180 – i = 148
h = 49.3.
Parallel lines remain the same distance apart.
Transversal
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Angles between Parallel LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Angles between Parallel LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
Draw a pair of parallel lines with a transversal and measure the 8 angles.
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Angles between Parallel LinesAngles between Parallel Lines
Angles between Parallel LinesAngles between Parallel Lines
Angles between Parallel LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
ad c
egh
f
Name an angle corresponding to the marked angle.
Angles between Parallel LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a bc
egh
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a bc
h g
d
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a b
e
h g
d
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a b
e
h g
d
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a b
e
h g
d c
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a b
eh g
d
c
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 LinesAngles between Parallel Lines
Parallel lines remain the same distance apart.
Transversal
a b
e
h g
d c
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 LinesAngles between Parallel Lines
a
f
ehg
d
cName 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 LinesAngles between Parallel Lines
a
f
eb g
d
cName 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 LinesAngles between Parallel Lines
h
f
eb g
d
cName 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 LinesAngles between Parallel Lines
hf
e
b
g
d
c
Name in order, the angles that are alternate, interior and 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 LinesAngles between Parallel Lines
a
fe
hg
dc
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Name in order, the angles that are alternate, interior and corresponding to the marked angle.
Angles between Parallel LinesAngles between Parallel Lines
x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
100o Find the unknown angles stating reasons, from the list below.
y
z
60o
x =
y =
z =
Angles between Parallel LinesAngles between Parallel Lines
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
Finding unknown angles
105o
Find the unknown angles stating reasons, from the list below.
y
z
x =
y =
z =
55o
Angles between Parallel LinesAngles between Parallel Lines
x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
95o Find the unknown angles stating reasons, from the list below.
y
60o
Unknown angles in
quadrilaterals and other figures can be found
using these properties.
Angles between Parallel LinesAngles between Parallel Lines
x
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Finding unknown angles
Find the unknown angles stating reasons, from the list below.
y
55o z
x =
y =
z =
What does this tell you about parallelograms?
Unknown angles in
quadrilaterals and other figures can be found
using these properties.
Angles between Parallel LinesAngles between Parallel Lines
70o
a
Vertically opposite angles are equal.
Corresponding angles are equal.
Alternate angles are equal.
Interior angles sum to 180o .(Supplementary)
Find the unknown angles stating reasons, from the list below. There may be more than one reason.
58o
b
dc
Angle sum of a triangle (180o)
Angle on a line sum to (180o)
efg
h
Base angles isosceles triangle equal.
Angles at a point sum to 360o
Mixing it!
Angles between Parallel LinesAngles between Parallel Lines
Angle FactsAngle Facts
Now do these:
65o
p
99o
77o
38o
54o
48o
35o
z
130o
y
x
wt u
s
r
q
vCorresponding angles
p = 65o
Alternate angles
q = 38o
Corresponding angles
r = 77o
Opposite angles (with r)or Alternate angles with 77o
s = 77o
t = 99o
v = 54o
u = 81o
w = 126o
x = 130o
y = 130o
z = 35o + 48o = 83o
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