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The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …

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Presentation on theme: "The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …"— Presentation transcript:

1 The Great Angle Chase There are many different pathways that lead to the same destination. Here is just one of them …

2 J I L M N K O S P Q R T U G H 25  100  35  Aim: To write in the size of every angle.

3 J I L M N K O S P Q R T U G H 25  100  35  Look for the angle between a tangent and a chord. Locate the angles in the alternate segment. 25 

4 J I L M N K O S P Q R T U G H 100  35  25 

5 J I L M N K O S P Q R T U G H 100  35  25  35  Look for angles in the same segment.

6 J I L M N K O S P Q R T U G H 25  100  35  25  35 

7 J I L M N K O S P Q R T U G H 25  100  35  Look for angles standing on equal chords. 25  35 

8 J I L M N K O S P Q R T U G H 25  100  35  25  35 

9 J I L M N K O S P Q R T U G H 25  100  35  Look for right angles: 25  The angle between a tangent and a radius The angle in a semicircle 65  40  35 

10 J I L M N K O S P Q R T U G H 25  100  35  25  65  40  35 

11 J I L M N K O S P Q R T U G H 25  100  35  Look for triangles: 25  65  40  35  Angle sum 55  40  55  75 

12 J I L M N K O S P Q R T U G H 25  100  35  Look for triangles: 25  65  40  35  Angle sum 55  40  55  75  120 

13 J I L M N K O S P Q R T U G H 25  100  35  Look for triangles: 25  65  40  35  Angle sum Exterior angle 55  40  55  75  125  75  120 

14 J I L M N K O S P Q R T U G H 25  100  35  Look for triangles: 25  65  40  35  Angle sum Exterior angle 55  40  55  75  125  60  75  120 

15 J I L M N K O S P Q R T U G H 25  100  35  Look for vertically opposite angles and angles at a point. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60 

16 J I L M N K O S P Q R T U G H 25  100  35  And there’s another triangle. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15 

17 J I L M N K O S P Q R T U G H 25  100  35  And then another pair of angles in the same segment. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15 

18 J I L M N K O S P Q R T U G H 25  100  35  Some more right angles. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  40 

19 J I L M N K O S P Q R T U G H 25  100  35  Aha! A cyclic quadrilateral. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  40 

20 J I L M N K O S P Q R T U G H 25  100  35  More angles at a point. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  100  80  100  40 

21 J I L M N K O S P Q R T U G H 25  100  35  25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  100  80  100  40 

22 J I L M N K O S P Q R T U G H 25  100  35  Another angle between a tangent and a chord. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  100  80  100  40 

23 J I L M N K O S P Q R T U G H 25  100  35  A cyclic quadrilateral. 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  100  80  100  40  65 

24 J I L M N K O S P Q R T U G H 25  100  35  And we’re done! 25  65  40  35  55  40  55  75  125  60  120  60  80  100  125  75  105  75  120  60  15  75  80  100  80  100  40  65 


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