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More Lessons for Geometry

Common Core For Geometry

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**

- Given circle π΄ with π΅πΆ β₯ π·πΈ, πΉπ΄ = 6, and π΄πΆ = 10. Find π΅πΉ and π·πΈ. Explain your work.
- If two arcs in a circle have the same measure, what can you say about the quadrilateral formed by the four endpoints? Explain.
- Find the angle measure of πΆπ· and πΈπ· .

**Exercises**

- Given circle π΄ with ππ΅πΆ = 54Β° and β πΆπ·π΅ β β π·π΅πΈ, find ππ·πΈ. Explain your work.
- If two arcs in a circle have the same measure, what can you say about the quadrilateral formed by the four endpoints? Explain.
- Find the angle measure of πΆπ· and πΈπ·
- ππΆπ΅ = ππΈπ· and ππ΅πΆ : ππ΅π· : ππΈπΆ = 1: 2: 4. Find the following angle measures. a. πβ π΅πΆπΉ b. πβ πΈπ·πΉ c. πβ πΆπΉπΈ
- π΅πΆ is a diameter of circle π΄. ππ΅π· : ππ·πΈ : ππΈπΆ = 1: 3: 5. Find the following arc measures. a. ππ΅π· b. ππ·πΈπΆ c. ππΈπΆπ΅

**Lesson Summary**

**Theorems:**

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

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