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Download Lesson 3: Inscribed Angle Theorem and Its Applications (CC lesson 5)
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Lesson 3 NYS COMMON CORE MATHEMATICS CURRICULUM M5 GEOMETRY Name___________________ Period: _______ Date__________ Lesson 3: Inscribed Angle Theorem and Its Applications (CC lesson 5) Learning Target οΆ I can use relationships among central angles, inscribed angles, and the intercepted arcs. Opening Exercises (7 minutes) π¨ and πͺ are points on a circle with center πΆ. a. Draw a point π© on the circle so that Μ Μ Μ Μ π¨π© is a diameter. Then draw the angle π¨π©πͺ. b. What angle in your diagram is an inscribed angle? c. What angle in your diagram is a central angle? d. How can we distinguish between the inscribed and central angles? e. What is the difference between a chord and a radius? f. What is an arc? Minor and Major arc Minor_____________________ What is the intercepted arc ? What is the intercepted arc of β π¨πΆπͺ ? Major______________ Lesson 3 NYS COMMON CORE MATHEMATICS CURRICULUM M5 GEOMETRY Name___________________ Period: _______ Date__________ Example 1. Use the diagram on the right to answer all the questions a. Μ Μ Μ Μ π¨π© , Μ Μ Μ Μ π¨π« πππ Μ Μ Μ Μ π¨πͺ are all ___________ b. What type of triangle is β πͺπ¨π« ? c. What is the mathematical connection between β πͺπ¨π©, β π¨πͺπ« πππ β π¨π«πͺ? d. The measure of the inscribed angle π¨πͺπ« is π, and the measure of the central angle πͺπ¨π© is π. Find πβ πͺπ¨π© in terms of π. e. What is true about β πͺπ¨π©, β π¨πͺπ« ? Example 2. For the diagram on the right answer all the questions below a. β π΄π΅πΆ ππ ____________ β π΄ππΆ ππ ____________ b. What is the intercepted arc ππ β ABC ? Μ , β AOC and β ABC ? c. What is the connection of the measure of minor AC In conclusion β¦.. οΆ The measure of the CENTRAL ANGLE is ___equal_______ to the measure of the intercepted arc. οΆ The measure of the Inscribed Angle is _____1/2_______ the measure of the intercepted angle. Lesson 3 NYS COMMON CORE MATHEMATICS CURRICULUM M5 GEOMETRY Name___________________ Period: _______ Date__________ Example 3. In each of the following diagrams of circle O, the measure of πβ πΆππ΄ = 50°, find πβ πΆπ΅π΄. a. b. Μ Μ Μ Μ and Μ Μ Μ Μ Μ = 56°. Example 4. Given circle A with diameters π΅πΆ π·πΈ and ππΆπ· A. What is the measure of β πΆπ΄π·? B. What is the measure of β πΆπ΅π·? Μ? C. What is the degree measure of πΆπ΅π· c. Lesson 3 NYS COMMON CORE MATHEMATICS CURRICULUM M5 GEOMETRY Name___________________ Period: _______ Date__________ Lesson 3: Inscribed Angle Theorem and Its Applications (CC lesson 5) Classwork 1. Find the measure of β π in each of the diagrams below. b. πβ π· = 15° a. πβ π· = 25° π π c. πβ π΅ = 32° d. πβ π· = 19° Lesson 3 NYS COMMON CORE MATHEMATICS CURRICULUM M5 GEOMETRY Name___________________ Period: _______ Date__________ 2. Examine the inscribed polygon below. Express π in terms of π and π in terms of π. Are the opposite angles in any quadrilateral inscribed in a circle supplementary? Explain. 3. Find the value of x in each of the diagrams below 4. Find the measures of β π in the diagram at right. 5. Find each measure. πβ πΏπ½π = _______ πβ πΏπΎπ = _______ Μ = _______ ππΏπ NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 3 M5 GEOMETRY Name___________________ Period: _______ Date__________ Lesson 3: Inscribed Angle Theorem and Its Applications (CC lesson 5)
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