Honors Geometry Circle Investigation - Instructions
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1 Honors Geometry ircle Investigation - Instructions 1. On the first circle a. onnect points and O with a line segment. b. onnect points O and also. c. Measure O. d. Estimate the degree measure of by using the fact that the points are 10 apart. e. ill in the blank for ircle onjecture #1 f. onnect points and. g. onnect points and. h. Measure. i. ill in the blank for ircle onjecture #2 j. onnect points and. k. onnect points and. l. Measure. m. ill in the blank for ircle onjecture #3 2. On the second circle a. raw diameter. b. onnect points and. c. onnect points and. d. Measure. e. onnect points and. f. onnect points and. g. Measure. h. ill in the blank for ircle onjecture #4 3. On the third circle a. onnect any 4 letters to make a quadrilateral. b. Measure each angle. c. ill in the blank for ircle onjecture #5 4. On the fourth circle a. Using your straight edge, draw a tangent line from point to point G. b. raw a radius from point G to the center of the circle. c. Measure GO. d. ill in the blank for ircle onjecture #6 e. Using your straight edge, draw a tangent line from point to point H. f. Measure the distance from point to each point of tangency. g. ill in the blank for ircle onjecture #7 Honors Geometry ircles 2 Name: lock: ate: h. Lay a straight edge over the circle so one side of it lines up with any two points. i. raw down each side of the straight edge, making two parallel lines. j. Estimate the degree measure of each intercepted arc by using the fact that the points are 10 apart. k. ill in the blank for ircle onjecture #8
2 5. On the fifth circle a. Use your straight edge to connect points and. b. Use your straight edge to connect points and. c. In centimeters, measure. Write this measurement inside the circle, near. d. In centimeters, measure. Write this measurement inside the circle, near.. e. Using the fact that the points on the circle are 10 apart, count the degree measure of. f. Put this measurement outside the circle, near. g. Using the fact that the points on the circle are 10 apart, count the degree measure of. h. Put this measurement outside the circle, near. i. Use your straight edge to connect points E and. j. Use your straight edge to connect points G and H. k. Measure your new segments and their arcs. l. Put these measurements in the appropriate places on your sketch. m. Notice the relationships among the measurements on your paper. n. ill in the blanks for ircle onjecture #9 and ircle onjecture #10 6. On the sixth circle. a. hoose any point on the circle and label it E. b. raw a line that passes through points and E. c. Measure E with your protractor. d. ount the degree measure of the arc that is intercepted by E. e. Measure E with your protractor. f. ount the degree measure of the arc that is intercepted by E. g. Notice the relationship between the arc measure and the angle measure. h. ill in the blank for ircle onjecture #11 7. On the seventh circle. a. onnect points and to create a chord. b. onnect points and to create a chord. c. Label their intersection point E. d. Measure E with your protractor. e. Measure E with your protractor. f. ount the measure of. g. ount the measure of. h. Notice the relationship between the arc measurements and angle measurements. i. ill in the blank for ircle onjecture #12 8. On the eighth circle a. onnect points and to create a secant. b. onnect points and to create a secant. c. Extend these lines until they meet to form an angle outside the circle. d. Measure the angle with your protractor. e. ount the measure of one of the arcs intercepted by this angle. f. ount the measure the other arc intercepted by this angle. g. Notice the relationship between the arc measurements and the angle measurements. h. ill in the blanks for ircle onjecture #13
3 Honors Geometry ircle Investigation ircles irst ircle Name: lock: ate: ircle onjecture #1 The measure of a central angle is the as the measure of the arc it intercepts. O ircle onjecture #2 The measure of an inscribed angle is the measure of the arc it intercepts. ircle onjecture #3 Inscribed angles that intercept the same arc are Second ircle ircle onjecture #4 ngles inscribed in a semicircle are angles.
4 ircle onjecture #5 Opposite angles of a quadrilateral inscribed in a circle are. Third ircle E G ircle onjecture #6 tangent to a circle is to the radius drawn to the point of tangency. ircle onjecture #7 Tangent segments to a circle from a point outside the circle are. ourth ircle O H ircle onjecture #8 Parallel lines intercept arcs on a circle.
5 E G ircle onjecture #9 If two arcs are congruent, then their are congruent. ifth ircle O ircle onjecture #10 If two chords are congruent, then their are congruent. H Sixth ircle ircle onjecture #11 n angle formed by a tangent ray and a secant is always the measure of the arc it intercepts.
6 Seventh ircle ircle onjecture #12 The measure of an angle formed by two intersecting chords is the of the measures of the arcs that are intercepted by it and its vertical angle. ircle onjecture #13 The measure of an angle formed by two secants that intersect outside a circle is of the arcs intercepted by it. Eighth ircle
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