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Transcript
Name: ______________________________________________________________
Date: ______________________ Period: ______
Chapter 13: Circle Arcs & Angles
Topic 1: Angle Relationships – Central & Inscribed
1) Central Angle
The degree measure of an arc is ________________________________
___________________________________________________________
__________________________________________________________
Μ‚ =___________.
If π‘š < 𝐴𝑃𝐡 = 60°, then π‘šπ΄π΅
According to the provided circle:
Major Arc = _______________
Minor Arc = ______________
A circle gets it’s name from the center. Therefore, the diagram above is called Circle P.
Examples:
1)
Μ‚ = _______________
π‘šπ΄π΅
4)
2)
3)
Μ‚ = _______________
π‘šπ΄π΅
π‘š < 𝐴𝑃𝐡 = ______________
Given: Circle P, π‘š < 𝐡𝑃𝐢 = 15°
Find:
a) π‘š < 𝐴𝑃𝐢 = ____________________
Μ‚ = ___________________
b) π‘š 𝐴𝐢
Μ‚ = ___________________
c) π‘š 𝐡𝐢
Μ‚ = ___________________
d) π‘š 𝐴𝐡
Μ‚ = ___________________
e) π‘š 𝐴𝐡𝐢
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2) Inscribed Angle
To find the measure of an inscribed angle, we _____________________
__________________________________________________________.
Formula: ________________________________________
Examples:
Μ‚ = 140°
1) Find π‘š < 𝐴 when π‘š 𝐡𝐢
Μ‚ = 60°
2) Find π‘š < 𝑁 when π‘š 𝑀𝑂
Μ‚ = ________________
3) Find π‘š 𝐴𝐢
π‘š < 𝐴 = ______________
π‘š < 𝐢 = ______________
Μ‚ = _______________
π‘š 𝐴𝐡
Mixed Examples (Common Core)
4) In the figure below, O is the center of the circle and segment AD is a diameter.
a.) Find m<AOB.
b.) If m<AOB:m<COD = 3:4, what is m<BOC?
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5) In the circle shown, BC is a diameter with center A. m<CBE = 26o and m<BDA = 18o.
Μ‚.
a.) Find the measure of 𝐢𝐸
b.) Find m<BAE.
c.) Find m<DAB.
6) The diagram below is of Circle A. Use the information given to find the measure of the labeled angles.
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Name: ______________________________________________________________
Date: ______________________ Period: ______
Topic 1: Angle Relationships – Central & Inscribed
Complete the following examples. Show all work, including formulas for free-response questions. A correct
answer with no work shown will not receive credit on a test or quiz.
1.) In the diagram below of circle O, m<ABC = 24. What is the m<AOC?
(1) 12
(2) 24
(3) 48
(4) 60
2.) As shown in the diagram below, quadrilateral DEFG is inscribed in a circle and m<D = 86.
Μ‚.
a.) Determine and state 𝐺𝐹𝐸
b.) Determine and state m<F.
3.) Given Circle A, the m<B = 32o. Find m<ACD.
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Μ‚ : 𝐢𝐸
Μ‚ : 𝐸𝐷
Μ‚ : 𝐷𝐡
Μ‚ = 1: 2: 3: 4. Find the following measures.
4.) In circle A, 𝐡𝐢
Μ‚
a.) π‘šπΈπ·
b.) m<BAC
c.) m<DAE
Μ‚
d.) π‘šπΆπΈπ·
Μ‚ = π‘šπ΅πΉ
Μ‚ and <FED = 66o.
5.) Use the diagram below to find the measure of <BCD. Given: π‘šπ·π΅
Review Questions:
6.) What are the coordinates of the midpoint of the line segment with endpoints (2,-5) and (8,3)?
(1) (3,-4)
(2) (3,-1)
(3) (5,-4)
(4) (5,-1)
7.) If two sides of a triangle have lengths of 4 and 10, the third side could be
(1) 8
(2) 2
(3) 16
(4) 4
8.) Write an equation of a line that is parallel to the line whose equation is 3y = x + 6 and passes through the
point (-3,4)
9.) Quadrilateral HYPE has vertices H(2,3), Y(1,7), P(-2,7), and E(-2,4). State and label the coordinates of the
vertices H”Y”P”E” after the composition transformations π‘Ÿπ‘₯βˆ’π‘Žπ‘₯𝑖𝑠 ∘ 𝑇5,βˆ’3.
10.) The sum of the interior angles of a regular polygon is 540o. Determine and state the number of degrees
in one interior angle of the polygon.
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