Circle theorem 5 and 6 07.01.14.

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Presentation transcript:

Circle theorem 5 and 6 07.01.14

Introduction

The Alternate Segment Theorem. The angle between a tangent and a chord through the point of contact is equal to the angle subtended by that chord in the alternate segment. 45o xo yo 60o zo Find the missing angles below giving reasons in each case. angle x = angle y = angle z = xo yo yo xo 45o (Alt Seg) 60o (Alt Seg) Th5 75o angle sum triangle

Find angle ATS and angle TSR B TSR = 70 T 70 R 80 A 70 S

Find angle ATS and angle TSR B TSR = 70 T 70 80 ATS = 80 R 80 A Set the pupils some examples to do. 70 S

Cyclic Quadrilateral Theorem. The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180o) w y Th6 r p x z s q Angles x + z = 180o Angles p + r = 180o Angles y + w = 180o Angles q + s = 180o

Find the missing angles below given reasons in each case. Cyclic Quadrilateral Theorem. Theorem 6 The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180o) 85o 110o x y 70o 135o p r q Find the missing angles below given reasons in each case. angle x = angle y = angle p = angle q = angle r = 180 – 85 = 95o (cyclic quad) 180 – 135 = 45o (straight line) 180 – 110 = 70o (cyclic quad) 180 – 70 = 110o (cyclic quad) 180 – 45 = 135o (cyclic quad)

Angles in a cyclic quadrilateral Drag the points around the circumference of the circle to demonstrate this theorem. Hide some of the angles, modify the diagram and ask pupils to calculate the sizes of the missing angles.

Start the clip at 2.32 mins