Circles

Lesson 6

Math

Unit 7

10th Grade

Lesson 6 of 14

Objective


Determine the angle and length relationships between intersecting chords.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • G.SRT.A.2

Criteria for Success


  1. Describe and apply the property that when two chords intersect each other inside the circle, the sum of the intercepted arcs equals the sum of the vertical angles formed by the intersection. See Unit 7 Glossary for visual. 
  2. Describe and apply the Intersecting Chords Theorem, which states that when two chords intersect each other inside the circle, the product of the segments of each intersected chord are equal. See Unit 7 Glossary for visual.
  3. Prove the Intersecting Chords Theorem using similarity of triangles. 

Tips for Teachers


  • The following tool is useful for this lesson in order to show the relationship between intercepted arcs and the angles formed by interesting chords: GeoGebra, Kayclan, “Angles Formed by Intersecting Chords."
  • The following tool is useful for this lesson in order to show the relationship between the line segments of intersecting chords: Math Open Reference, “Intersecting Chord Theorem."
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Anchor Problems

25-30 minutes


Problem 1

Use the diagram below to determine the relationship between the intercepted arcs of intersecting chords.

Guiding Questions

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Problem 2

What is the relationship between the product of $$EF \cdot FB $$ and $$CF \cdot FD$$?

Guiding Questions

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Target Task

5-10 minutes


Use the diagram below, which is not drawn to scale.

  1. Lowell says that $$m\angle DFC=\frac{1}{2}(123)=61^\circ$$ because it is half of the intercepted arc. Sandra says that you cannot determine the measure of $$\angle DFC$$ because you do not have enough information. Who is correct and why?
  2. If $$m\angle EFC=9^\circ$$, find and explain how you find $$m\angle BFE$$ and $$m\widehat{BE}$$.

References

EngageNY Mathematics Geometry > Module 5 > Topic C > Lesson 14Exit Ticket

Geometry > Module 5 > Topic C > Lesson 14 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..

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

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

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Equations of Circles

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

Topic C: Arc Length, Radians, and Sector Area

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