Download Lesson 5: Inscribed Angle Theorem and Its Applications

Lesson 5
COMMON CORE MATHEMATICS CURRICULUM
M5
GEOMETRY
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Lesson 5: Inscribed Angle Theorem and Its Applications
Classwork
Opening Exercises
1.
2.
𝐴 and 𝐶 are points on a circle with center 𝑂.
a. Draw a point 𝐵 on the circle so that ̅̅̅̅
𝐴𝐵 is a diameter. Then
draw the angle 𝐴𝐵𝐶.
b.
What angle in your diagram is an inscribed angle?
c.
What angle in your diagram is a central angle?
d.
What is the intercepted arc of ∠𝐴𝐵𝐶?
e.
What is the intercepted arc of ∠𝐴𝑂𝐶?
The measure of the inscribed angle 𝐴𝐶𝐷 is 𝑥, and the measure of the
central angle 𝐶𝐴𝐵 is 𝑦. Find 𝑚∠𝐶𝐴𝐵 in terms of 𝑥.
Lesson 5:
Date:
Inscribe Angle Theorem and Its Applications
4/6/15
1
Lesson 5
COMMON CORE MATHEMATICS CURRICULUM
M5
GEOMETRY
Exercises 1–4
1.
Find the measure of the angle with measure 𝑥.
a.
𝑚∠𝐷 = 25°
b.
𝑚∠𝐷 = 15°
c.
𝑚∠𝐵𝐴𝐶 = 90°
x
x
d.
x
𝑚∠𝐵 = 32°
e.
Lesson 5:
Date:
𝑚∠𝐸𝐴𝐶 = 60°
Inscribe Angle Theorem and Its Applications
4/6/15
f.
𝑚∠𝐷 = 19°
2
COMMON CORE MATHEMATICS CURRICULUM
Lesson 5
M5
GEOMETRY
2.
Toby says △ 𝐵𝐸𝐴 is a right triangle because 𝑚∠𝐵𝐸𝐴 = 90°. Is he correct? Justify your answer. Do not assume
Toby’s measurement is correct.
3.
Examine the diagram below. How many angles have the same measure?
What is the maximum inscribed angle measurement that is possible? ________
Lesson 5:
Date:
Inscribe Angle Theorem and Its Applications
4/6/15
3
Lesson 5
COMMON CORE MATHEMATICS CURRICULUM
M5
GEOMETRY
4.
Find the measures of the labeled angles.
a.
b.
c.
d.
e.
f.
Lesson 5:
Date:
Inscribe Angle Theorem and Its Applications
4/6/15
4
Lesson 5
COMMON CORE MATHEMATICS CURRICULUM
M5
GEOMETRY
Lesson Summary
Theorems:

THE INSCRIBED ANGLE THEOREM: The measure of a central angle is twice the measure of any inscribed angle
that intercepts the same arc as the central angle.

CONSEQUENCE OF INSCRIBED ANGLE THEOREM: Inscribed angles that intercept the same arc are equal in
measure.
Relevant Vocabulary

INSCRIBED ANGLE: An inscribed angle is an angle whose vertex is on a circle, and each side of the angle
intersects the circle in another point.

INTERCEPTED ARC: An angle intercepts an arc if the endpoints of the arc lie on the angle, all other points of
the arc are in the interior of the angle, and each side of the angle contains an endpoint of the arc. An
angle inscribed in a circle intercepts exactly one arc, in particular, the arc intercepted by a right angle is
the semicircle in the interior of the angle.
Problem Set
Answers are given but you must explain how you got the answer.
1. 𝒙 = 𝟑𝟒, 2. x=94, 3.𝒙 = 𝟑𝟎, 4. 𝒙 = 𝟕𝟎 5. 𝒙 = 𝟔𝟎, 6. x=60, 7. x=20, 8.𝒙 = 𝟒𝟔. Look to use the same arc based on information given in
the problem. Highlight what you know.
For Problems 1–8, find the value of 𝑥.
1.
2.
Lesson 5:
Date:
Inscribe Angle Theorem and Its Applications
4/6/15
5
Lesson 5
COMMON CORE MATHEMATICS CURRICULUM
M5
GEOMETRY
3.
4.
5.
6.
7.
8.
Lesson 5:
Date:
Inscribe Angle Theorem and Its Applications
4/6/15
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