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Lesson Plans and Worksheets for Geometry
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More Lessons for Geometry
Common Core For Geometry
Student Outcomes
Secant Lines; Secant Lines That Meet Inside a Circle
Classwork
Opening Exercise
π·π΅ is tangent to the circle as shown. a. Find the values of π and π. b. Is πΆπ΅ a diameter of the circle? Explain.
Exercises 1β2
Example
a. Find π₯. Justify your answer. b. Find π₯.
We can state the results of part (b) of this example as the following theorem: SECANT ANGLE THEOREMβINTERIOR CASE: The measure of an angle whose vertex lies in the interior of a circle is equal to half the sum of the angle measures of the arcs intercepted by it and its vertical angle.
Exercises 3β7
In Exercises 3β5, find π₯ and οΏ½ 6. In the circle shown, π΅πΆ is a diameter. Find π₯ and π¦. 7. In the circle shown, π΅πΆ is a diameter. π·πΆ: π΅πΈ = 2: 1. Prove π¦ = 180 β 3/2 π₯ using a two-column proof.
Lesson Summary
THEOREMS:
SECANT ANGLE THEOREMβINTERIOR CASE: The measure of an angle whose vertex lies in the interior of a circle is equal to half the sum of the angle measures of the arcs intercepted by it and its vertical angle.
Relevant Vocabulary
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