Lesson 4 | Circles | 10th Grade Mathematics

Objective

Define a chord to derive the Chord Central Angles Conjecture and Thales’ Theorem.

Lesson Map

Topic A: Equations of Circles

Lesson

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

Lesson

Given a circle with a center translated from the origin, write the equation of the circle and describe its features.

Standards

G.C.A.1G.CO.A.5G.GPE.A.1

Lesson

Write an equation for a circle in standard form by completing the square. Describe the transformations of a circle.

Standards

G.CO.A.5G.GPE.A.1

Topic B: Angle and Segment Relationships in Inscribed and Circumscribed Figures

Lesson

Define a chord to derive the Chord Central Angles Conjecture and Thales’ Theorem.

Standards

G.C.A.2

Lesson

Describe the relationship between inscribed and central angles in terms of their intercepted arc.

Standards

G.C.A.2

Lesson

Determine the angle and length relationships between intersecting chords.

Standards

G.C.A.2

Lesson

Prove properties of angles in a quadrilateral inscribed in a circle.

Standards

G.C.A.3

Lesson

Define and determine properties of tangents and secants of circles to solve problems with inscribed and circumscribed triangles.

Standards

G.C.A.2G.C.A.3

Lesson

Construct tangent lines to a circle to define and describe the circumscribed angle.

Standards

G.C.A.2G.C.A.4

Lesson

Use angle and side length relationships with chords, tangents, inscribed angles, and circumscribed angles to solve problems.

Standards

G.C.A.2

Topic C: Arc Length, Radians, and Sector Area

Lesson

Define, describe, and calculate arc length.

Standards

G.C.B.5

Lesson

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.

Standards

G.C.B.5

Lesson

Calculate the sector area of a circle. Identify relationships between sector area, arc angle, and radius.

Standards

G.C.B.5

Lesson

Use sector area of circles to calculate the composite area of figures.

Standards

G.C.B.5N.Q.A.2N.Q.A.3

Circles

Objective

Lesson Map

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Circles

Objective

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