Angles in a Triangle




















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Opposite Angles of Cyclic Quad =




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Exterior Angle of Cyclic Quad




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Angle at Centre

Note that "Angle in Semi Circle" is a special case of the angle at the centre being twice the angle at the circumference.

Play with the model on the LHS and note that this rule has three distinct forms (arrowhead, "bow" and small quadrilateral).




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Tangent Perpendicular to Radius

Look out for radii / tangents. These are always perpendicular to each other!




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Angle Same Arc / Chord

Investigate the model below. Explain why shifting the "move me" point between points A and C "breaks" the model.




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Vertically Opposite Angles (Y9)

This one works, as long as you have two straight lines intersecting each other (rather than four short lines joining at a common point)




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