Arcs and Chords

New York State Common Core Math Geometry, Module 5, Lesson 8

Worksheets for Geometry, Module 5, Lesson 8

Student Outcomes

• Congruent chords have congruent arcs, and the converse is true.
• Arcs between parallel chords are congruent.

Arcs and Chords

Classwork

Opening Exercise

1. Given circle 𝐴 with 𝐵𝐶 ⊥ 𝐷𝐸, 𝐹𝐴 = 6, and 𝐴𝐶 = 10. Find 𝐵𝐹 and 𝐷𝐸. Explain your work.
2. If two arcs in a circle have the same measure, what can you say about the quadrilateral formed by the four endpoints? Explain.
3. Find the angle measure of 𝐶𝐷 and 𝐸𝐷 .

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Exercises

1. Given circle 𝐴 with 𝑚𝐵𝐶 = 54° and ∠𝐶𝐷𝐵 ≅ ∠𝐷𝐵𝐸, find 𝑚𝐷𝐸. Explain your work.
2. If two arcs in a circle have the same measure, what can you say about the quadrilateral formed by the four endpoints? Explain.
3. Find the angle measure of 𝐶𝐷 and 𝐸𝐷
4. 𝑚𝐶𝐵 = 𝑚𝐸𝐷 and 𝑚𝐵𝐶 : 𝑚𝐵𝐷 : 𝑚𝐸𝐶 = 1: 2: 4. Find the following angle measures. a. 𝑚∠𝐵𝐶𝐹 b. 𝑚∠𝐸𝐷𝐹 c. 𝑚∠𝐶𝐹𝐸
5. 𝐵𝐶 is a diameter of circle 𝐴. 𝑚𝐵𝐷 : 𝑚𝐷𝐸 : 𝑚𝐸𝐶 = 1: 3: 5. Find the following arc measures. a. 𝑚𝐵𝐷 b. 𝑚𝐷𝐸𝐶 c. 𝑚𝐸𝐶𝐵

Lesson Summary

Theorems:

• Congruent chords have congruent arcs.
• Congruent arcs have congruent chords.
• Arcs between parallel chords are congruent.

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