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
- 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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