Download Chapter 8 Quiz Review Sheet – Circles

Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
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Chapter 8 Quiz Review Sheet – Circles Students Will Be Able To: • Use proportional reasoning to determine the lengths of arcs of circles and the area of sectors of circles (TB 8.07) • Prove and use theorems about chords (TB 8.09) • Prove and use the relationship between inscribed angles and their corresponding central angles. (TB 8.10) • Prove and use theorems about chords and inscribed angles. (TB 8.10) • Prove and use properties of cyclic quadrilaterals (TB 8.11) • Prove and use theorems about tangents. (TB 8.12) Theorems You Should Know (and be able to use): 1. If two central angles are congruent, then their intercepted arcs are congruent. 2. If two arcs are congruent, then they are intercepted by congruent central angles. 3. If two arcs are congruent, then their corresponding chords are congruent. 4. If two chords are congruent, then their corresponding arcs are congruent. 5. Congruent chords are equidistant from the center of the circle. 6. The measure of an inscribed angle is equal to half the measure of its intercepted arc. 7. If a line through the center of a circle is perpendicular to a chord, then it bisects the chord. 8. If a line through the center of a circle bisects a chord, then it is perpendicular to the chord. 9. If a line is the perpendicular bisector of a chord, then the line passes through the center of the circle. 10. Inscribed angles are congruent if and only if they intercept the same arc or congruent arcs. 11. Any angle inscribed in a semicircle is a right angle. 12. The opposite angles of a cyclic quadrilateral are supplementary. 13. Tangent segments from a point outside the circle to the circle are congruent. 14. A tangent of a circle is perpendicular to a radius drawn to the point of tangency. 1 Math 2: Algebra 2, Geometry and Statistics
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Practice Problems: Part 1: Tangent Properties 2 Math 2: Algebra 2, Geometry and Statistics
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Part 2: Chord Properties In the diagrams below, find each unknown. 1. 2. 3. 4. 5. Name:
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3 Math 2: Algebra 2, Geometry and Statistics
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Part 3: Arcs and Angles 1. 2. 3. 4. 4 Math 2: Algebra 2, Geometry and Statistics
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Part 4: Arc Length 4. 7. 8. 5. 6. 5 Math 2: Algebra 2, Geometry and Statistics
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Part 5: Proofs 3. In the following diagram, 𝐴𝐵 ≅ 𝐴𝐶. Prove AMON is a kite. 6