Friday 25 March 2022 Friday 25 March 2022 Created by Mr Lafferty Created by Mr Lafferty 1 Circles Circles Revision of Angle Properties Angles in a semi-circle www.mathsrevision.com Pythagoras Theorem (S O H)(C A H)(T O A) Tangent line on a circle National 4 Isosceles Triangles in Circle
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Monday, 08 June 2015Monday, 08 June 2015Monday, 08 June 2015Monday, 08 June 2015Created by Mr Lafferty1 Circles Revision of Angle Properties Angles in.
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Tuesday 18 April 2023Tuesday 18 April 2023 Created by Mr Lafferty Created by Mr Lafferty 11
CirclesCircles
Revision of Angle Properties
Angles in a semi-circle
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Pythagoras Theorem
(SOH)(CAH)(TOA)
Tangent line on a circle
National 4
Isosceles Triangles in Circles
Tuesday 18 April 2023Tuesday 18 April 2023 Created by Mr Lafferty Created by Mr Lafferty 22
Starter QuestionsStarter Questionsw
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o o o
1. Find the length the hypotenuse.
2. Find sin(c ), cos(c ) and tan(c ) f or triangle in Q1
3. What is the name of the shape with this net.
4. Calculate the value of the missing angle. 34o
A
B
C
6
8co
National 4
18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
1.1. To identify isosceles To identify isosceles triangles with circles.triangles with circles.
1. To investigate isosceles triangles with circles.
2.2. Solve problems using Solve problems using angle properties.angle properties.
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RevisionRevisionAngle PropertiesAngle Properties
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When two radii are drawn to the ends of a chord, When two radii are drawn to the ends of a chord, An isosceles triangle is formed.An isosceles triangle is formed.
C
A B
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mIsosceles triangles Isosceles triangles
in Circlesin Circles
xo xoDEMO
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Special Properties of Isosceles Triangles
Two equal lengths
Two equal angles
Angles in any triangle sum to 180o
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mIsosceles triangles Isosceles triangles
in Circlesin Circles
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Q.Q.Find the angle xFind the angle xoo..
A
B
C
SolutionAngle at C is equal to:
Since the triangle is isosceleswe have
360 280 80o o o
xo
280o
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mIsosceles triangles Isosceles triangles
in Circlesin Circles
2 80 180o o ox
2 100o ox
50o ox
18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Now try Ex 1Ch12 (page 137)Copy out shapes
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RevisionRevisionAngle PropertiesAngle Properties
National 4
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Starter QuestionsStarter Questionsw
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o o o
1. Find the length the hypotenuse.
2. Find sin(b ), cos(b ) and tan(b ) f or triangle in Q1
3. What is the name of the shape with this net.
4. Calculate the value of the missing angle.
A
B
C
5
12
bo
27o
National 4
18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
1.1. To know when to use To know when to use Trigonometry (STrigonometry (SOOHCHCAAHTHTOOA) A) to calculate length and to calculate length and
angles angles within a circlewithin a circle..
1. To explain how we can use Trigonometry (SOHCAHTOA) to calculate length and angles within a circle.
2.2. Solve problems using Solve problems using Trigonometry (STrigonometry (SOOHCHCAAHTHTOOA) A) ..
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Angles in a Semi CircleAngles in a Semi CircleSOHCAHTOANational 4
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National 4
Angles in a Semi-CircleAngles in a Semi-Circle
We have been interested in right angled triangles withina semi-circle. Since they are right angled we can useSOHCAHTOA to calculate lengths and angles.
Example 1 : Calculate the value of angle xo
o O 3tan = =
A 4x
1 3
4tanox
36 9ox .
P
A B
4cm3cm
d cm
xo=36.9o
SOHCAHTOA
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mAngles in a Semi-CircleAngles in a Semi-Circle
B
A C67.4o
13 cm
Example 2 : Calculate the length of AB
13cos o A AB
xH
13 67 4cos . oAB
5AB cm
5cm
SOHCAHTOANational 4
National 4
18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Now try Ex 3Ch12 (page 140)
Q10 onwardsSketch shapes
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Angles in a Semi-CircleAngles in a Semi-Circle
SOHCAHTOA
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If a = 7 b = 4 and c = 10
Write down as many equations as you can
Starter QuestionsStarter Questions
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e.g. a + b + c = 21
National 4
18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty