Unit 7: Circles

Students investigate the geometry of circles, including chords, arcs, central and inscribed angles, tangents, cyclic quadrilaterals, inscribed and circumscribed circles of triangles, sector area, arc length, and radian measure.

Choose a worksheet

PDFs open in a new tab. Print or save them from your browser. Use the paired answer guide to check your work. No login needed.

Unit

Review the unit’s main ideas.

📝 Open worksheet PDF ✅ Open answer guide PDF

Concept

Start with the core idea.

📝 Open worksheet PDF ✅ Open answer guide PDF

Practice

Build fluency with more questions.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

Advanced

Try more challenging problems.

Set 1

📝 Open worksheet PDF ✅ Open answer guide PDF

Set 2

📝 Open worksheet PDF ✅ Open answer guide PDF

What this unit covers

A Lines, Angles, and Circles · 3 lessons

Goals

• Determine measures of central angles, inscribed angles, and arcs.
• Use the relationship between radii, chords, and tangent lines to prove geometric theorems.

Lessons

1. Lines, Angles, and Curves
2. Inscribed Angles
3. Tangent Lines

B Polygons and Circles · 4 lessons

Goals

• Construct the inscribed and circumscribed circles of a triangle.
• Prove properties of the angles in a quadrilateral inscribed in a circle.

Lessons

1. Quadrilaterals in Circles
2. Triangles in Circles
3. A Special Point
4. Circles in Triangles

C Measuring Circles · 6 lessons

Goals

• Comprehend that the radian measure of an angle whose vertex is the center of a circle is the ratio of the length of the arc defined by the angle to the circle’s radius.
• Coordinate between representations of angles measured in degrees and in radians.
• Generalize methods for calculating lengths of arcs and areas of sectors in circles.

Lessons

1. Arcs and Sectors
2. Part to Whole
3. Angles, Arcs, and Radii
4. A New Way to Measure Angles
5. Radian Sense
6. Using Radians

D Let’s Put It to Work · 1 lesson

Lessons

1. Putting It All Together

Helpful to know first

The curriculum says this unit builds on these.

Grade 7 Math · Unit 3 Measuring Circles

Open unit →