Curriculum / Math / 10th Grade / Unit 7: Circles / Lesson 5
Math
Unit 7
10th Grade
Lesson 5 of 14
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Lesson Notes
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Describe the relationship between inscribed and central angles in terms of their intercepted arc.
The core standards covered in this lesson
G.C.A.2 — Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
The foundational standards covered in this lesson
7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
In the diagram below, $$\angle CAB$$ is a central angle, $$\angle CDB$$ is an inscribed angle, and $$\widehat{CB}$$ is an intercepted arc.
The two diagrams below also show that $$\angle CAB$$ is a central angle, $$\angle CDB$$ is an inscribed angle, and $$\widehat{CB}$$ is an intercepted arc.
What is the angle measure that represents $$\widehat{EB}$$?
Given that $$\triangle BCD$$ is inscribed in circle $$A$$, determine the relationship between $$\angle t$$ and $$\angle y$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Given circle $$A$$ with diameters $$\overline{BC}$$ and $$\overline{DE}$$ and $$m\widehat{CD}=56^\circ$$,
Geometry > Module 5 > Topic B > Lesson 7 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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Determine the angle and length relationships between intersecting chords.
Topic A: Equations of Circles
Derive the equation of a circle using the Pythagorean Theorem where the center of the circle is at the origin.
Standards
G.GPE.A.1G.GPE.B.4
Given a circle with a center translated from the origin, write the equation of the circle and describe its features.
G.C.A.1G.CO.A.5G.GPE.A.1
Write an equation for a circle in standard form by completing the square. Describe the transformations of a circle.
G.CO.A.5G.GPE.A.1
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Topic B: Angle and Segment Relationships in Inscribed and Circumscribed Figures
Define a chord to derive the Chord Central Angles Conjecture and Thales’ Theorem.
G.C.A.2
Prove properties of angles in a quadrilateral inscribed in a circle.
G.C.A.3
Define and determine properties of tangents and secants of circles to solve problems with inscribed and circumscribed triangles.
G.C.A.2G.C.A.3
Construct tangent lines to a circle to define and describe the circumscribed angle.
G.C.A.2G.C.A.4
Use angle and side length relationships with chords, tangents, inscribed angles, and circumscribed angles to solve problems.
Topic C: Arc Length, Radians, and Sector Area
Define, describe, and calculate arc length.
G.C.B.5
Describe the proportional relationship between arc length and the radius of a circle. Convert between degrees and radians to write the arc measure in radians.
Calculate the sector area of a circle. Identify relationships between sector area, arc angle, and radius.
Use sector area of circles to calculate the composite area of figures.
G.C.B.5N.Q.A.2N.Q.A.3
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