Targets
- 8A. Prove that all circles are similar by showing that for a dilation centered at the center of a circle, the preimage and the image have equal central angle measures.
- 8B. Describe the relationship between a central angle, inscribed angle, and circumscribed angle and the arc they intercept.
- Recognize that an inscribed angle with sides that intersect the endpoints of the diameter of a circle is a right angle.
- Recognize that the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
- 8C. Given a triangle construct an inscribed circle and a circumscribed circle.
- Construct an inscribed circle with a center at the point of intersection of the angle bisectors.
- Construct the circumscribed circle with a center at the point of intersection of the perpendicular bisectors of each side of the triangle.
- 8D. Explain and utilize the properties of arcs.
- Apply the Arc Addition Postulate to solve for missing arc measures.
- Use similarity to calculate the length of an arc.
- Prove that opposite angles in an inscribed quadrilateral are supplementary.
- Define the radian measure of an angle as the ratio of an arc length to its radius and calculate a radian measure when given an arc length and its radius.
- Calculate the area of a sector.
- 8E. Identify the center and radius of a circle given its equation.
- 8F. Define and identify a tangent line and construct a tangent line from a point outside the circle using construction tools or computer software
Essential Questions
- How can the properties of circles, polygons, lines and angles be useful when solving geometric problems?
- How can algebra be useful when expressing geometric properties?
Class Notes
http://www.mathsisfun.com/geometry/constructions.html
Link for April 29, 2014 notes
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Important Files
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