PROPERTIES OF CIRCLES

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Step 1:Guided Investigation 7.9CYCLIC QUADRILATERALSStart with a circle on a patty paper andfold a cyclic quadrilateral., ,,,Step 2: Trace your cyclic quadrilateral on anotherpatty paper.Step 3: Rotate and slide the copy over the originaland look for any relationships between pairsof angles.AV,"Step 4: Copy a pair of opposite angles so that theyshare a vertex and a side. Do this with theother pair of opposite angles. What do younotice about the sum of the measures of theangles in each case?Step 5: Repeat steps 1-4 with another cyclic quadrilateral., ,, ,~, ' , ,, ,,,, , , ,,,';f .Compare your results with the results of others near you. Your next patty paper conjecture could be:\ 0,,'-r:bla~ 52 The sum of the measures of a pair of opposite angles in a cyclic quadrilateral is _ _ _1 14 INVEST1GATlON SET 7
c::J Open Investigation 7.'~ FINDING THE CENTER <strong>OF</strong> A CIRCLEBefore you begin the circle investigations you should take a supply of patty papers and construct alarge circle on each one. (A dozen will do.) Use a compass with a felt-tip pen or use a cup or glass as atemplate to make the circles.Step 1:Draw a circle on a patty paper. (If possible,do not use a compass.) See if you can discovera way to find the center of the circle by folding.Describe your method for finding the center of the circle.oStep 2:Step 3:Step 4:Step 5:Step 6:Step 7:Step 8:Take out another patty paper with a circle on it. Fold or draw two chords on your circle.Fold the perpendicular bisector of each chord.Use your compass to verify that the point of intersection of the perpendicular bisectors is thecenter of the circle.On another patty paper use your compass to draw an arc of a circle.Fold or draw two chords on your arc.Fold the perpendicular bisector of each chord, and mark the point of intersection of the twoperpendicular bisectors.Use your compass to verify that this point is the center of the circle that contains the arc youdrew in step 5.Use your results to write a conjecture about the point of intersection of the perpendicular bisectors oftwo different chords of a circle (or an arc of a circle).~44<strong>PROPERTIES</strong> Of CIRruS "5
Page 1 and 2: INVESTIGATION SET 7PROPERTIES OF CI
Page 4 and 5: Guided Inyestlgatlon 7. I continued
Page 8 and 9: Step 1:Guided Invesligalion 7.5INSC
Page 10 and 11: c:::J ~G~u~id=.~d~l=n~y~.=sl~ig~a='
Page 14 and 15: ~Step 1:Open Investigation 7.2~..!!
Page 16 and 17: c::::J Open Investigation 7.6~ ANGL
Page 18 and 19: EXERCISE SET 7 ASketch and carefull
Page 20 and 21: EXERCISE SET 7CUse your patty paper
Page 22 and 23: ~ ~3. AB and A C are tangents.m8 Fk
Page 24 and 25: EXERCISE SET 6E1. more than one pos
Page 26: EXERCISE SET 7E1. more than one pos

PROPERTIES OF CIRCLES

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