Home›Lesson Plans›Mathematics›Geometry · Grade 10

Circles: Arcs, Chords & Angles

Tenth graders explore the anatomy of circles — radii, chords, and arcs — and the angle relationships within them, discovering that a central angle equals its arc while an inscribed angle is exactly half.

Grade 10Circles55 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Name the parts of a circle.
  • ✓Relate a central angle to its arc.
  • ✓Relate an inscribed angle to its arc.
  • ✓Identify chords and arcs.
Essential Question

A circle looks simple — but it’s full of hidden relationships. How do the angles, arcs, and chords inside a circle connect to each other?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Circle Explorer · Interactive

The Circle Explorer

Project this and tap each part of a circle. Have students learn how central and inscribed angles relate to arcs!

⭕ Explore circles — tap each partTry it

The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Hidden Relationships

5 min

A circle looks simple — but what relationships hide inside?

👩‍🏫 Teacher Moves

  • Show a circle with an angle.
  • Ask about the connections.
  • Set the goal: circles.

🎒 Student Actions

  • See the circle.
  • Wonder the links.
  • Predict them.
2

I Do — Angles & Arcs

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Name the parts.
  • Central angle = its arc.
  • Inscribed angle = half the arc.

🎒 Student Actions

  • Learn the parts.
  • Learn central angles.
  • Learn inscribed angles.
3

We Do — Explore Together

13 min

Class uses the Circle Explorer.

👩‍🏫 Teacher Moves

  • Tap each part.
  • Relate angles to arcs.
  • Identify chords.

🎒 Student Actions

  • Tap each part.
  • Relate them.
  • Find chords.
4

You Do — On Your Own

12 min

Students find measures.

👩‍🏫 Teacher Moves

  • Find arc and angle measures.
  • Use the inscribed-angle rule.
  • Identify parts.

🎒 Student Actions

  • Find measures.
  • Use the rule.
  • Identify parts.
5

Close — Close

5 min

One circle.

👩‍🏫 Teacher Moves

  • Show a circle problem.
  • Find a missing measure.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find it.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School Geometry).

CCSS
G-C.2

Identify and describe relationships among inscribed angles, radii, and chords.

CCSS
G-C.1

Prove that all circles are similar.

CCSS
G-C.5

Find arc lengths and areas of sectors.

CCSS
G-CO.1

Know precise definitions of geometric figures.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Circle-part diagram.
  • Sentence frame: “An inscribed angle is ___ its arc.”
  • Use labeled circle cards.

Support & Access

IEP / 504
  • Start with central angles.
  • Use a labeled diagram.
  • Focus on the parts first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find sector area and arc length.
  • Prove the inscribed-angle theorem.
  • Solve chord problems.
Materials

What to gather

  • 📽️Projector / board
  • 📐Compasses
  • 💻The Circle Explorer
  • 📄Circle diagrams
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

circleall points equidistant from a centerradiuscenter to the edgediameteracross, through the centerchorda segment joining two points on the circlearca portion of the circle’s edgecentral anglevertex at the centerinscribed anglevertex on the circlecircumferencethe distance around
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
If a central angle measures 80°, what is the measure of its intercepted arc?
80° (a central angle equals its arc).
QUESTION 2
An inscribed angle intercepts an arc of 100°. What is the angle’s measure?
50° (half the arc).
QUESTION 3
What is the longest chord in a circle?
The diameter.

Going deeper? Sectors.

Have students find the area of a sector and the length of an arc using the central angle as a fraction of the whole circle. A printable circles sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Circles: Arcs, Chords & AnglesFlip
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Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Circles: Arcs, Chords & AnglesQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Circles: Arcs, Chords & AnglesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: arc, central angle, chord, circle, circumference, diameter, inscribed angle, radius
  1. vertex on the circle
  2. a segment joining two points on the circle
  3. a portion of the circle’s edge
  4. center to the edge
  5. the distance around
  6. vertex at the center
  7. across, through the center
  8. all points equidistant from a center

Part B · Show what you learned

  1. If a central angle measures 80°, what is the measure of its intercepted arc?
  2. An inscribed angle intercepts an arc of 100°. What is the angle’s measure?
  3. What is the longest chord in a circle?
Answer key — Part A: 1) inscribed angle · 2) chord · 3) arc · 4) radius · 5) circumference · 6) central angle · 7) diameter · 8) circle
Part B: 1) 80° (a central angle equals its arc). 2) 50° (half the arc). 3) The diameter.