9.1 and 9.2 Introduction to Circles

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1 Date: Secondary Math 2 Vocabulary 9.1 and 9.2 Introduction to Circles Define the following terms and identify them on the circle: Circle: The set of all points in a plane that are equidistant from a given point Center of the circle: Radius: Diameter: Chord: Secant: Tangent: Point of Tangency: Central Angle: Inscribed Angle: Arc: Major Arc: Minor Arc: Semicircle:

2 Identify the indicated part of the circle. Explain your answer. Identify each angle as an inscribed angle or central angle. Use the diagram to the right. a) Angle URE b) Angle ZOM Angle URE = Angle ZOM = Classify each arc as a major arc, a minor arc, or a semicircle. Use the diagram to the right. a) AAAA b) BBBBBB c) AAAA a) AAAA b) BBBBBB c) AAAA Draw the part of a circle that is described. 1. a) Chord AB b) Central angle AOB 2. a) Inscribed angle GGGGGG b) The point of tangency J Ex 1) Ex 2)

3 9.2 Vocabulary Degree Measure of a minor arc: Determine the degree measure of each minor arc. Determine the measure of each central angle. Vocabulary Adjacent Arcs: Intercepted Arc: Arc Addition Postulate: a) In circle A, arcs BC and CD are adjacent arcs. So BBBBBB = + Inscribed Angle Theorem: Determine the measure of each inscribed angle.

4 Determine the measure of each intercepted arc. Calculate the measure of each angle. Parallel Lines-Congruent Arcs Theorem: Use the given information to answer each question

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6 Date: Secondary Math and 9.4 Measuring Angles Inside and Outside of Circles Interior angles of a Circle Theorem: If an angle is formed by two intersecting or secants such that the of the angle is in the of the circle, then the measure of the angle is the sum of the measures of the intercepted by the angle and its vertical angle. Write an expression for the measure of the given angles. Exterior Angles of a Circle Theorem: If an angle is formed by two intersecting, two intersecting tangents, or an intersecting tangent and secant such that the of the angle is in the of the circle, then the measure of the angle is the difference of the measures of the arc(s) intercepted by the angle. List the intercepted arc(s) for the given angles. Write an expression for the measure of the given angle.

7 Tangent to a Circle Theorem: A line drawn to a circle is perpendicular to a of the circle drawn to the point of tangency. 9.4 Vocabulary Diameter- Chord Theorem: If a circle s diameter is to a chord, then the diameter the chord and bisects the determined by the chord. Use the given information to answer each question. Explain your answer. What else do you know is true in the figure? Equidistant chord Theorem: If two of the same circle or congruent circles are, then they are from the center of the circle. Equidistant chord Converse Theorem: If two of the same circle or congruent circles are from the center of the circle, then the chords are.

8 Congruent chord-congruent Arc Theorem: If two of the same circle or congruent circles are, then their corresponding arcs are. Congruent chord-congruent Arc Converse Theorem:: If two of the same circle or congruent circles are, then their corresponding are congruent. Compare each measurement. Segments of a Chord: the formed on a chord when two chords of a circle. Segment Chord Theorem: : If two chords in a circle, then the of the lengths of the segments of one is equal to the of the lengths of the segments of the chord. Use each diagram and the Segment Chord Theorem to write and equation involving the segments of the chords. Open you skills practice to 9.3 # 20. We will do this proof together.

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10 Date: Secondary Math 2 Vocabulary 9.5 and 10.1 Tangents and Secants Define the following terms and identify the corresponding parts of the figure. External Secant Segment: Secant Segment: Calculate the measure of each angle. Explain your reasoning. Tangent Segment Theorem: Write a statement to show the congruent segments

11 Secant segment Theorem: Calculate the measure of each angle. Explain your reasoning Name two secant segments and two external secant segments for circle O. Use each diagram and the Secant Segment Theorem to write and equation involving the secant segments Name a tangent segment, a secant segment, and an external secant segment for circle O.

12 Secant Tangent Theorem: Use each diagram and the Secant Tangent Theorem to write an equation involving the secant and tangent Inscribed Right Triangle-Diameter Theorem: Inscribed Right Triangle-Diameter Converse Theorem: Draw a triangle inscribed in the circle through the three points. Then determine if the triangle is a right triangle. Draw a triangle inscribed in the circle through the given points. Then determine the measure of the indicated angle.

13 Inscribed Quadrilateral-Opposite Angles Theorem: Draw a quadrilateral inscribed in the circle through the given four points. Then determine the measure of the indicated angle. Construct a circle inscribed in each polygon.

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