4-Aug-15Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles Finding Missing angles...
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Transcript of 4-Aug-15Created by Mr.Lafferty Math Dept Revising Basic Angles Naming Angles Finding Missing angles...
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Revising Basic Angles
Naming Angles
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Finding Missing angles
Angles in a Triangle
Corresponding Angles
Alternate Angles
AnglesAnglesNational 4 REL 1.2c
Angles in a Quadrilateral
Drawing Triangles
Measuring Angles
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter QuestionsStarter Questions
Q3. Calculate 2.34 + 4.7 + 0.12
Q1. Convert to the 24 hour clock. (a) 7:25 pm (b) 6:50 am
Q2. Write down the type of angle that is less than 90 deg.
Q4. Round the following to nearest 1000.
(a) 12,501 (b) 369,765
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National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to identify acute, To be able to identify acute, right-angle, obtuse, straight right-angle, obtuse, straight line and reflex angles.line and reflex angles.
1. To revise Type of Angles.
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Type of AnglesType of AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Acute less than 90o
Obtuse Between 90o – 180o
Right Angle exactly 90o
reflex over 180o less than 360o
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Straight Line Angle exactly 180o
Type of AnglesType of Angles
HorizontalV
ertica
l
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 (page 14)
Exercise 1
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Type of AnglesType of AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter QuestionsStarter Questionsw
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Q3. Calculate 5.65 – 1.3
Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40
Q2. Write down 2 numbers that add to give 8 andmultiply to give 15.
Q4. Round the following to nearest 100.
(a) 13,551 (b) 369,449
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to name an To be able to name an angle.angle.
1. To explain how we name angles by THREE capital letters with the angle sign. The middle letter being where the angle is.
2.2. Understand the Understand the difference between the difference between the type of angle and the type of angle and the name of an angle.name of an angle.
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Naming AnglesNaming AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Naming AnglesNaming Anglesw
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A
B C
Type of angle is acute
Name of angle is ∠ ABC
Type of angle is obtuse
Name of angle is ∠ ZYX
X
YZ
MIDDLE LETTER IS ALWAYS WHERE THE ANGLE IS
ALWAYS 3 CAPITAL LETTERS
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 (page 15)
Exercise 2
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Naming AnglesNaming AnglesNational 4 REL 1.2c
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 1010
Starter QuestionsStarter Questions
Q3. List the prime numbers between 10 and 20.
Q1. Convert to the 12 hour clock. (a) 17:15 (b) 05:40
Q2. Write down lowest common multiple of 3, 4 , 5.
Q4. Round the following to nearest 100.
(a) 13,551 (b) 369,449
19 Apr 2023 11
A 180o Protractor
Outside scale from 0o to 180o going in a clockwise direction.
Inside scale from 0o to 180o going in an
anti-clockwise direction.
19 Apr 2023 12
You need to be able to measure an angle to the nearest degree. To help you do this you should always:1. Look directly down onto the cross point.
2. Always use the protractor in a horizontal manner as shown below.
19 Apr 2023 13
1
2
Measuring Angles with a
180o Protractor
0 on the outside so use outside
scale
0 on the inside so use inside scale
67o
50o
19 Apr 2023 14
3
4
Measuring Angles with a
180o Protractor
0 on the outside so use outside
scale
0 on the inside so use inside scale
135o
120o
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 (page 17)
Exercise 3
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Naming AnglesNaming AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter Starter QuestionsQuestions
(a) - 6 - 7 (b) -10 + (-3) (c) - 2 - 12
Q2. Convert to 12 hrs clock
(a) 23 00 hrs (b) 14 23 hrs
Q.3 Solve 5x - 45=70
1. Calculate:
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National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know 360To know 360oo in a circle. in a circle.1. To calculate missing angle give all other angles. 2.2. Find missing angle Find missing angle
given all other angles.given all other angles.
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Find Missing AnglesFind Missing AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
120o 95
o
Find Missing Find Missing AngleAngle
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Angles round a pointalways add up to 360
o
65o
Two angles making astraight line add up to 180
o
(Supplementary angles)
Angles opposite each otherat a cross are equal.
34o 34
o
115o
146o
146o 145o
35o
Two angles making aright angle add up to 90
o
(Complementary angles)
55o
National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 1919
x 47o
1
114o
y
2
3 4
76o
a82o
b
Angle x = 180 – 47 = 133
o
Angle y = 180 – 114 = 66o
Angle a = 180 – 76 = 104o
Angle b = 180 – 82 = 98ow
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Angles and Angles and TrianglesTriangles
National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 2020
Angle xo = 360
o - (90
o + 100
o +
105o)
90100105+295
Example
Find angle x.360o
105o
100ox
oThink !
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Angles and TrianglesAngles and Triangles
= 360o – 295
o = 65
o
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 (page 20)
Exercise 4
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Find Missing Find Missing AngleAngle
National 4 REL 1.2c
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 2222
(SAS) Starter Questions(SAS) Starter Questions
Q3. Calculate the missing angles.80
o
Q1. Convert the percentages to fractions.
(a) 30% (b) 60%
Q2. Write down all the factors of 16.
Q4. Round the following to 1 decimal place.
(a) 4.549 (b) 6.551
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 2323
Drawing SAS TrianglesDrawing SAS Triangles
SAS TrianglesSAS Triangles
AngleAngle SideSideSideSide
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 2424
Drawing SAS TrianglesDrawing SAS Triangles
Toolkit required
1.1.RulerRuler
2.2.ProtractorProtractor
3.3.Pencil & PaperPencil & Paper
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Created by Mr. Lafferty 2525
Drawing SAS TrianglesDrawing SAS Triangles
Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30o and AC = 5cm
Step 1 Draw line AB=6cm
A B
CStep 2 Measure
angle CAB from A
Step 3 Draw the line AC = 5cm
through X. Label it C.
Step 4 Join C to B.
Check angles add to 180o
A B
C
30o
X
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 (page 22)
Exercise 5
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Find Missing Find Missing AngleAngle
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter Starter QuestionsQuestions
1. Solve the equation 5x- 3=18 (decimal value)
2. Calculate (- 13)+(- 1)- 15
3. Calculate x:
4. Change 790cm into m
5. What is the coordinate C(- 8,- 4) reflected in the x- axis?
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75o
xo
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Sum of Angles in a Sum of Angles in a TriangleTriangle
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know all angles in a To know all angles in a triangle add to 180triangle add to 180oo
..1. To show that all the
angles in a triangle sum to 180
o.
2.2. Use knowledge to solve Use knowledge to solve problems.problems.
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National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
To determine the
angle sum of any Triangle
Cut off corners
Cut off corners
Cut off corners
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National 4 REL 1.2c
Apr 19, 2023 Created by Mr.Lafferty Math Dept
angle sum of any Triangle
All angles in a triangle ALWAYS
added up to180o
180o
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National REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 3131
Equilateral Triangle Isosceles triangle Right-angled triangle
Angles and TrianglesAngles and Trianglesw
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3 equal sides
3 equal angles.
2 equal sides
2 equal angles (base)
One angle is 90o
National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 3232
Example 1
a
65o
Calculate angle a.
Angle a = 180 – (90 + 65)
= 180 – 155 = 25oExample
2Calculate angles a, b and
ca
b
cSince the triangle is equilateral,
angles a, b and c are all 60o
(180/3)
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National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 3333
Angle a = 65o (base angles of an isosceles triangle are equal).
a65o
Example 3Calculate angle a.
b
Angle b = 180 –(65 + 65)
= 180 – 130 = 50o
Example 4Calculate angles x and y
y
130o
x
180 - 130Angles x and y =
2o50
= =252
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National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr Lafferty Created by Mr Lafferty 3434
180 - 90Angles a and b =
2
Example 5Calculate angles a and
b.b
a
o90 = =45
2
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Isosceles triangle
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Sum of Angles in a Sum of Angles in a TriangleTriangle
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32o
50o
38o
87o
xo
xo x
o
xo
Remember all the angles add up to 180o
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ex 6 Ch2 (page 23)
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Sum of Angles in a Sum of Angles in a TriangleTriangle
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter Starter QuestionsQuestions
2 16 28 xQ1. Solve the equation below
Q2. Find two numbers that multiply to give 18and subtract to give 3.
Q3. Find the average and range of the numbers below
Q4. Find2,8,8,10
60% of £ 240
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National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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1.1. To understand the term To understand the term corresponding angles.corresponding angles.
1. To explain the term corresponding angles and show how we use the property to solve problems.
2. To be able to use property to solve problems.
AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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AnglesAnglesCorresponding Angles
Which angles are equal?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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AnglesAnglesCorresponding Angles
Which angles are equal?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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AnglesAnglesCorresponding Angles
Which angles are equal to the shaded angle?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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AnglesAngles
Which angles are equal to
the shaded angle?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
look for
shapes
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AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
120
x120
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AnglesAngles
What is the value of letter x?
Corresponding AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
100
a100
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AnglesAngles
What is the value of letter a?
Corresponding AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
48
b48
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AnglesAngles
What is the value of letter b?
Corresponding AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
110
c110
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AnglesAngles
What is the value of letter c?
Corresponding AnglesNational 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
70
a
70
b110
What are the values of letters a and b?
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AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
115
65115 65 What are the values of
the missing angles?
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AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
57
123
57
123
What are the values of the missing
angles?
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AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 Extension Booklet
Ex7E Page 1 Q1 to Q4
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AnglesAnglesCorresponding AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Starter Starter QuestionsQuestions
4 7 9 x
Q1. Solve the equation below
Q2. Find two numbers that multiply to give 48and divide to give 3.
Q3. Find missing angles119o
ao
bo
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National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Deptww
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1.1. To understand the term To understand the term alternate angles.alternate angles.
1. To explain the term alternate angles and show how we use the property to solve problems.
2. To be able to use property to solve problems.
AnglesAnglesAlternate AnglesNational 4
REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Look for
- Z shapes
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AnglesAnglesAlternate Angles
= equal angles
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
35
a35
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AnglesAnglesAlternate Angles
Find the value of a ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
b
43
43
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AnglesAnglesAlternate Angles
Find the value of b ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
33
33c
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AnglesAnglesAlternate Angles
Find the value of c ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
123
d123
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AnglesAnglesAlternate Angles
Find the value of d ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
50
ab130 50
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AnglesAnglesAlternate Angles
Find the value a and b ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
135
c45
d
45
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AnglesAnglesAlternate Angles
Find the value of a and b ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
60
ab
c120
60120
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AnglesAnglesAlternate Angles
Find the value a, b and c ?
National 4 REL 1.2c
Apr 19, 2023Apr 19, 2023 Created by Mr.Lafferty Math DeptCreated by Mr.Lafferty Math Dept
Now try Ch2 Extension Booklet
Ex7E Page 4 Q5 to Q7
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AnglesAnglesAlternate AnglesNational 4
REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 6363Created by Mr.LaffertyCreated by Mr.Lafferty
Q3. Express the following percentages as fractions
Starter Starter QuestionsQuestions
35100
2 4 22x
Q1. List 4 properties of a square.
Q2. Simplify the following fraction
Q4. Solve
( ) 25% (b) 12.5%a
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National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023
Angles in a Quadrilateral
and ABC ACD
IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360o
C
DA
B
We have split the quadrilateral into two triangles
But for any triangle the sum of the angles is 180
0
Hence for the quadrilateral we have 2 x 180o=360
o
ao
cob
o
do
360o o o o oa b c d
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National 4 REL 1.2c
Wednesday 19 April 2023Wednesday 19 April 2023 6565Created by Mr.LaffertyCreated by Mr.Lafferty
Angles in a Quadrilateral
90 34 100 360o o o o oy
360 224o o oy
Question : Find the missing angle below.
x
yz
w34
o
100o
The four angles of a quadrilateral add to = 360o
136o oyy
o
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National 4 REL 1.2c