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Starter Questions B 5 A C 12 27o 1 1

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**To investigate the special angle in a semi-circle.**

Angles in a Semi Circle Learning Intention To investigate the special angle in a semi-circle.

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**Angles in a Semi Circle Tool-kit required 1. Protractor 2. Pencil**

3. Ruler 3

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**Angles in a Semi Circle 1. Using your pencil trace round**

the protractor so that you have semi-circle. 2. Mark the centre of the semi-circle. You should have something like this. 4

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**Angles in a Semi Circle x x x x x x Mark three points**

Outside the circle x x x x x 2. On the circumference 3. Inside the circle

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**Angles in a Semi Circle Log your results in a table.**

For each of the points Form a triangle by drawing a line 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. Inside Circumference Outside 6

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**Angles in a Semi Circle x Online Demo x x < 90o = 90o > 90o**

Inside Circumference Outside < 90o = 90o > 90o 7

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**Angles in a Semi-Circle**

KeyPoint for Angles in a Semi-circle B A C 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 8

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**Angles in a Semi-Circle**

Example 1 : Sketch diagram and find all the missing angles. 20o Hints 43o Look for right angle triangles Remember ! Angles in any triangle sum to 180o 47o 70o 9 9

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**Angles in a Semi-Circle**

Example 2 : Sketch the diagram. (a) Right down two right angle triangles (a) Calculate all missing angles. D C 60o E 25o A B 10

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Example of Good Work Exercise Number Date 2 columns

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**Angles in a Semi-Circle**

Now try Ex 2 Ch12 (page 138) Sketch shapes

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Section 9.2 TANGENTS.

Section 9.2 TANGENTS.

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