# Arcs and Chords

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

Worksheets for Geometry

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 π΄ with π΅πΆ β₯ π·πΈ, πΉπ΄ = 6, and π΄πΆ = 10. Find π΅πΉ and π·πΈ. 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 πΆπ· and πΈπ· .

Exercises

1. Given circle π΄ with ππ΅πΆ = 54Β° and β πΆπ·π΅ β β π·π΅πΈ, find ππ·πΈ. 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 πΆπ· and πΈπ·
4. ππΆπ΅ = ππΈπ· and ππ΅πΆ : ππ΅π· : ππΈπΆ = 1: 2: 4. Find the following angle measures. a. πβ π΅πΆπΉ b. πβ πΈπ·πΉ c. πβ πΆπΉπΈ
5. π΅πΆ is a diameter of circle π΄. ππ΅π· : ππ·πΈ : ππΈπΆ = 1: 3: 5. Find the following arc measures. a. ππ΅π· b. ππ·πΈπΆ c. ππΈπΆπ΅

Lesson Summary

Theorems:

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

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