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A STORY OF FUNCTIONS Lesson 13 M5 - HONORS...
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M5 Lesson 13 GEOMETRY Lesson 13: The Inscribed Angle Alternate—A Tangent Angle Exercises Find , , , , and/or . 1. 2. A STORY OF FUNCTIONS S.95 ©2015 Great Minds. eureka-math.org GEO-M5-SE-1.3.0-08.2015
Transcript of A STORY OF FUNCTIONS Lesson 13 M5 - HONORS...
M5 Lesson 13 GEOMETRY
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
Exercises
Find 𝑥𝑥, 𝑦𝑦, 𝑎𝑎, 𝑏𝑏, and/or 𝑐𝑐.
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A STORY OF FUNCTIONS
S.95
©20 15 G re at Min ds. eureka-math.org GEO-M5-SE-1.3.0-08.2015
M5 Lesson 13 GEOMETRY
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
3.
4.
𝑎𝑎
𝑏𝑏
A STORY OF FUNCTIONS
S.96
©20 15 G re at Min ds. eureka-math.org GEO-M5-SE-1.3.0-08.2015
M5 Lesson 13 GEOMETRY
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
5.
A STORY OF FUNCTIONS
S.97
©20 15 G re at Min ds. eureka-math.org GEO-M5-SE-1.3.0-08.2015
M5 Lesson 13 GEOMETRY
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
Problem Set In Problems 1–9, solve for 𝑎𝑎, 𝑏𝑏, and/or 𝑐𝑐.
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Lesson Summary
THEOREMS:
CONJECTURE: Let 𝐴𝐴 be a point on a circle, let 𝐴𝐴𝐵𝐵�����⃗ be a tangent ray to the circle, and let 𝐵𝐵 be a point on the circle such that 𝐴𝐴𝐵𝐵�⃖���⃗ is a secant to the circle. If 𝑎𝑎 = 𝑚𝑚∠𝐵𝐵𝐴𝐴𝐵𝐵 and b is the angle measure of the arc
intercepted by ∠𝐵𝐵𝐴𝐴𝐵𝐵, then 𝑎𝑎 = 12 𝑏𝑏.
THE TANGENT-SECANT THEOREM: Let 𝐴𝐴 be a point on a circle, let 𝐴𝐴𝐵𝐵�����⃗ be a tangent ray to the circle, and let 𝐵𝐵 be a point on the circle such that 𝐴𝐴𝐵𝐵�⃖���⃗ is a secant to the circle. If 𝑎𝑎 = 𝑚𝑚∠𝐵𝐵𝐴𝐴𝐵𝐵 and 𝑏𝑏 is the angle measure of
the arc intercepted by ∠𝐵𝐵𝐴𝐴𝐵𝐵, then 𝑎𝑎 = 12 𝑏𝑏.
Suppose 𝐴𝐴𝐵𝐵���� is a chord of circle 𝐵𝐵, and 𝐴𝐴𝐵𝐵���� is a tangent segment to the circle at point 𝐴𝐴. If 𝐸𝐸 is any point other than 𝐴𝐴 or 𝐵𝐵 in the arc of 𝐵𝐵 on the opposite side of 𝐴𝐴𝐵𝐵���� from 𝐵𝐵, then 𝑚𝑚∠𝐵𝐵𝐸𝐸𝐴𝐴 = 𝑚𝑚∠𝐵𝐵𝐴𝐴𝐵𝐵.
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M5 Lesson 13 GEOMETRY
Lesson 13: The Inscribed Angle Alternate—A Tangent Angle
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10. 𝐵𝐵𝐵𝐵�⃖���⃗ is tangent to circle 𝐴𝐴. 𝐵𝐵𝐵𝐵���� is a diameter. Find the angle measurements. a. 𝑚𝑚∠𝐵𝐵𝐵𝐵𝐵𝐵 b. 𝑚𝑚∠𝐵𝐵𝐴𝐴𝐵𝐵 c. 𝑚𝑚∠𝐵𝐵𝐵𝐵𝐴𝐴 d. 𝑚𝑚∠𝐵𝐵𝐵𝐵𝐵𝐵 e. 𝑚𝑚∠𝐵𝐵𝐵𝐵𝐵𝐵
11. 𝐵𝐵𝐵𝐵���� is tangent to circle 𝐴𝐴. 𝐵𝐵𝐸𝐸���� is a diameter. Prove: (i) 𝑓𝑓 = 𝑎𝑎 and (ii) 𝑑𝑑 = 𝑐𝑐.
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