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Exploring Angles in a Semi-Circle: Investigative Learning

In this learning activity, students will investigate the unique properties of angles formed in a semi-circle. Using tools like a protractor, pencil, and ruler, students will trace a semi-circle, mark points both inside and outside the circle, and measure the angles formed by drawing lines to these points from the endpoints of the diameter. The key concept is that any triangle inscribed in a semi-circle will have a right angle at the circumference. This exercise reinforces the understanding that the angles in any triangle sum to 180 degrees.

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Exploring Angles in a Semi-Circle: Investigative Learning

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  1. Starter Questions B 5 C A 12 27o 1

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

  3. Angles in a Semi Circle Tool-kit required 1. Protractor 2. Pencil 3. Ruler 3

  4. You should have something like this. 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. 4

  5. Angles in a Semi Circle x x x x • Mark three points • Outside the circle x x x x x 2. On the circumference 3. Inside the circle

  6. Log your results in a table. Outside Circumference Inside Angles in a Semi Circle 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 6

  7. Outside Circumference Inside Angles in a Semi Circle x Online Demo x x = 90o > 90o < 90o 7

  8. B A C Angles in a Semi-Circle KeyPoint for Angles 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

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

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

  11. Example of Good Work Exercise Number Date 2 columns

  12. Angles in a Semi-Circle Now try Ex 2 Ch12 (page 138) Sketch shapes

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