PROPERTIES OF CIRCLES
PROPERTIES OF CIRCLES PROPERTIES OF CIRCLES
Guided Inyestlgatlon 7. I continuedFINDING THE CENTER OF A CIRClEStep 5: On another patty paper use your compassto draw an arc of a circle.Step 6: Fold or draw two chords on your arc.Step 7:Fold the perpendicular bisector of each chord,and mark the point of intersection of the folds.,,,Step 8: Use your compass to verify that this pointof intersection is the center of the circle thatcontains the arc you drew in step 5.Use your results to complete the following conjecture:17.:! The perpendicular bisectors of two chords of a circle (or an arc of a circle) intersect~44 atthe .This technique gives you an easy way to find the center of a circle when you only have an arc.'06 INVESllGA110N SET 7
Step 1:Guided Inve.tlgatlon 7.2TANGENTS TO A CIRCLETake one of your parry papers with a circledrawn on it and draw or fold a line thatappears to be a tangent to your circle. (Ifnecessary, make two small, pinched creasesto mark the center of your circle.),oStep 2: Fold a line that passes through the centerof your circle and the point of tangency.Step 3: Place the corner of another parry paper at theangle formed between the radius (or diameter)and the tangent. What do you observe?Step 4: Draw another tangent to the same circle and repeat steps 1 and 2.Compare your results with the results of others near you. Your next parry paper conjecture could be:~ A tangent to a circle is _____ _ _ __ to the radius (or diameter) drawn to the~ 45 point of tangency.In this investigation you eyeballed a tangent to the circle. You can use this conjecture to fold a tangentto a circle at a given point.Step 5: Take another patry paper with a circle on it.Fold a diameter and mark a point where thediameter intersects the circle.Step 6: Fold a line perpendicular to the diameter throughthe point where the diameter intersects the circle.This line should be tangent to the circle.,(]",, ' ,, , , ,,,PROPERTIES OF CIRClfS I 07
- Page 1 and 2: INVESTIGATION SET 7PROPERTIES OF CI
- 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 12 and 13: Step 1:Guided Investigation 7.9CYCL
- 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
Guided Inyestlgatlon 7. I continuedFINDING THE CENTER <strong>OF</strong> A CIRClEStep 5: On another patty paper use your compassto draw an arc of a circle.Step 6: Fold or draw two chords on your arc.Step 7:Fold the perpendicular bisector of each chord,and mark the point of intersection of the folds.,,,Step 8: Use your compass to verify that this pointof intersection is the center of the circle thatcontains the arc you drew in step 5.Use your results to complete the following conjecture:17.:! The perpendicular bisectors of two chords of a circle (or an arc of a circle) intersect~44 atthe .This technique gives you an easy way to find the center of a circle when you only have an arc.'06 INVESllGA110N SET 7
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