Use the data and a calculator to investigate the relationship between the diameter and circumference of a circle. Create a circle of different size, measure its diameter and circumference, and record your results. Measure its diameter and its circumference and record your results. Use dynamic geometry software to draw a circle.What happens to the central angle as the length of the chord decreases?.What happens to the central angle as the length of the chord increases?.What do you observe about the angles measures found for chords of the same length?.Draw and measure the angle formed by joining the endpoints of each chord to the center of the circle. On the circle draw four different chords of the chosen length. Choose a length between 0.5 and 3.5 inches. Use a compass or dynamic geometry software to draw a circle with center C and radius 2 inches.Drag the point to different locations on the diameter and make a conjecture. Through an arbitrary point on the diameter (not the center of the circle) construct a chord perpendicular to the diameter. Using dynamic geometry, draw a circle and its diameter.the relative lengths of chords as compared to their distance from the center of the circle.G.G.49 Investigate, justify, and apply theorems regarding chords of a circle:.Describe what happens to the centers if the triangle is a right triangle.Are the four centers ever collinear? If so, under what circumstances?.If a center is moved outside of the triangle, under what circumstances will it happen?. Do any of the four centers always remain inside the circle?.Use your sketch to answer the following questions: Using dynamic geometry software, locate the circumcenter, incenter, orthocenter, and centroid of a given triangle.Justify your conjectures.Įxploring Constructions with Geometer’s Sketchpad Measure the exterior angle at C and the sum of the interior angles at A and B. Extend this investigation by overlaying a line on side AC.Drag a vertex and make a conjecture about the sum of the interior angles of a triangle. Using a dynamic geometry system draw ΔABC similar to the one below.Construct an angle of 300 and justify your construction.Construct an equilateral triangle with sides of length b and justify your work.Write a proof that ray BF bisects ∠ABC.Step 2: With the compass point at D and then at E, draw two arcs with the same radius that intersect in the interior of ∠ABC.Label the intersection points D and E respectively. Step 1: With the compass point at B, draw an arc that intersects BA and BC.Then construct the bisector of ∠ABCby following the procedure outlined below: Use a straightedge to draw an angle and label it ∠ABC.Write a proof that segment CD is the perpendicular bisector of segment AB.Label the intersections of the two arcs C and D. Step 2: With the compass point at B, draw a large arc with the same radius as in step 1 so that the arc intersects the arc drawn in step 1 twice, once above AB and once below AB.Step 1: With the compass point at A, draw a large arc with a radius greater than ❚B but less than the length of AB so that the arc intersects AB.Then construct the perpendicular bisector of segment AB by following the procedure outlined below: Use a straightedge to draw a segment and label it AB.Library of Resources from the Math ForumĮxploring Constructions with Geometer’s Sketchpad.Workshop Guide with Step-by-Step Instructions.Key Curriculum Press Website for Educators.New York State Virtual Learning System.Geometer’s Sketchpad and the New Geometry Strands By: David M.
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