8.4 PROPERTIES OFCYCLIC QUADRILATERALS (CQ)
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EX: GIVEN THAT THE RADIUS OF THE CIRCLE IS15CM, FIND THE PERIMETER OF THE HEXAGON.
The interior angle of each triangle is 60
Each triangle is also an equilateral triangle
The perimeter of the hexagon will be the base x 6
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I) WHAT IS A CYCLIC QUADRILATERAL
Quadrilateral: a polygon with four sides
Square, rectangle, parallelogram, trapezoid…..
The sum of all the interior angles is equal to 360 degrees
Cyclic Quadrilateral (CQ)
A quadrilateral with all four vertices (corners) on thecircumference of the circle
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II) PROPERTIES OF A CQ
Opposite interior angles in a CQ add to 180 degrees
If ABCD is a CQ
Then opposite angles mustbe “Supplementary”
Then ABCD must be a CQ
If opposite angles are“Supplementary”
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PROOF: OPPOSITE ANGLES IN A CQ ARE SUPPLEMENTARY
Prove:
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EX: DETERMINE THE VALUE OF EACH ANGLE
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Exterior angles: angles created by the extension of oneside
The Exterior angle is equal to the opposite interior angle
Exterior Angle
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PRACTICE: DETERMINE THE VALUE OF EACH ANGLE
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CHALLENGE: DETERMINE THE VALUE “X” & “Y”
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