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11
Starter QuestionsStarter Questions
1. Find the length the hypotenuse.
2. What is the name of the shape with this net.
3. Calculate the value of the missing angle.
A
B
C
5
12
27o
Learning IntentionLearning Intention
To investigate the special angle in a semi-circle.
Angles in a Semi CircleAngles in a Semi Circle
33
Tool-kit required
1. Protractor
2. Pencil
3. Ruler
Angles in a Semi CircleAngles in a Semi Circle
44
1. Using your pencil trace roundthe protractor so that you have semi-circle.
2. Mark the centre of the semi-circle.
You should have something like this.
Angles in a Semi CircleAngles in a Semi Circle
Mark three points
1. Outside the circle
x xx
x x
x x
x
x
2. On the circumference
3. Inside the circle
Angles in a Semi CircleAngles in a Semi Circle
66
For each of the points
Form a triangle by drawing aline from each end of the diameter to the point.Measure the angle at the various points.
x
x
x
Log your results in a table. InsideCircumferenc
eOutside
Angles in a Semi CircleAngles in a Semi Circle
77
InsideCircumferenceOutside
xx
x
< 90o
> 90o
= 90= 90oo
Online Demo
Angles in a Semi CircleAngles in a Semi Circle
KeyPoint for Angles in a Semi-circle
Angles in a Semi-CircleAngles in a Semi-Circle
A triangle ABC within a semicircle with base the length of the diameter
will ALWAYS be right angled at P on the circumference.
Remember - Angles in any triangle sum to 180o
B
A C
99
Hints
Example 1 : Sketch diagram and find all the missing angles.
70o
Look for right angle triangles43o
20o
47o
Remember ! Angles in any triangle
sum to 180o
Angles in a Semi-CircleAngles in a Semi-Circle
Example 2 : Sketch the diagram.
Angles in a Semi-CircleAngles in a Semi-Circle
C
A B
D
25o
60o
(a) Right down two right angle triangles
(a) Calculate all missing angles.
E
2 columns
Date
Exercise Number
Example of Good Work
Now try Ex 2Ch12 (page 138)Sketch shapes
Angles in a Semi-CircleAngles in a Semi-Circle