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Common Core High School Geometry Teaching and Learning Resources

Domain: C: Circles

Common Core Math

Select the cluster for resources on this page:

  • C-A: Understand and apply theorems about circles

  • C-B: Find arc lengths and areas of sectors of circles

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C-A: Understand and apply theorems about circles

Standards:

 

Technology-enhanced investigations:

Mathwords.com: Math Dictionary: Key vocabulary for this domain.  Use with C-A and C-B:

Circle Central Angle Secant Line Sector
Radius Inscribed Angle Circumscribed Circle Arc of a Circle
Chord Circumscribed Angle* (GeoGebra applet) Inscribed Circle Segment of a Circle
Diameter Tangent Line Radian

 

CK-12:Geometry: concepts, videos, and practice exercises for learners to complete: Use with C-A.2.

Khan Academy: Geometry: Circles:

Khan Academy: Geometric Constructions, Tutorial videos:

Imagine Learning Classroom (formerly LearnZillion) subscription needed:

MathsIsFun.com: Constructions: This is a series of 17 animated geometric constructions, which learners would do with a compass, pencil, and straightedge only.  Among those are circle constructions to find a center, tangent lines from an external point, inscribed and circumscribed circles for triangles, circle touching three points, and a pentagon construction.  Aligns with C-A.3 and C-A.4.

Math Open Reference: Constructions: The site provides step-by-step animations of constructions with compass and straightedge.  The list is comprehensive for lines, line segments, angles, triangles, circles, arcs, ellipses, polygons, and non-Euclidean constructions.  The following align with C-A.3 and C-A.4:

NCTM Illuminations:

  • Incenter-Incircle: This applet allows you to find the incenter and incircle of a triangle, and provides a visual explanation of why it occurs where it does.
  • Circumcircle: Applet to construct the circumcircle about a triangle.
  • Simson Line: Applet to construct and explore the Simson line.

Thinking Mathematics: Tangent Theorems for Circles via Pythagoras: A YouTube video on two results from the geometry of circles that are easily proven using Pythagoras’ theorem.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 21 manipulatives addressing C-A.2, 10 manipulatives for C-A.3, and 1 manipulative for C-A.4.  Among those:

 

Multiple Choice:

MathsIsFun.com: Circle Theorems: Content reviews inscribed angle theorems, angles in quadrilaterals inscribed in circles, the 90 degree angle between a tangent line and the radius drawn to the point of tangency.  Examples are shown.  Learners then complete 10 multiple choice problems on those theorems.  Aligns with C-A.2 and C-A.3.

Constructed-response:

Khan Academy: Geometry: Circles: Practice questions with videos.

Performance tasks:

Illustrative Mathematics: Geometry:

Inside Mathematics: MARS Tasks:

  • Circle and Squares: Students calculate sides of squares given the radius of the inscribed and circumscribed circle and calculate ratios of nested circles and squares.  This task aligns with standards C-A.2 and C-A.3.
  • Circles in Triangles: Students use geometric properties of circles and triangles to prove that two triangles are congruent.  This task aligns with geometry congruence standards CO-C.9 and CO-C.10 and geometry circle standards C-A.2 and C-A.3.

Mathematics Assessment Project: High School: Geometry:

Mathematics Vision Project, Secondary 2 Student Edition:

 

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C-B: Find arc lengths and areas of sectors of circles

Standards:

 

Technology-enhanced investigations:

CK-12: Geometry: Arcs in Circles: concepts, videos, and practice problems for learners to complete.

Thinking Mathematics: Radian Measure: A YouTube video with explanation of the radian measure.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 10 manipulatives for C-B.5.  Among those:

Multiple Choice:

MathsIsFun.com: Circle Sector and Segment: Content reviews arc length and area of a sector showing how formulas are derived.  It also includes how to find the area of a segment.  Learners can complete 10 multiple choice problems.  Use with C-B.

Constructed-response:

Khan Academy: Geometry: Circles Practice questions with videos.

  • Arc measures in degrees: Aligns with C-B.5.
  • Arc Length: Relate the length of the arc to the circumference and the central angle subtended by the arc in degrees.  Aligns with C-B.5.
  • Radians and Degrees: Convert angle measures from degrees to radians and vice versa.  Aligns with C-B.5.
  • Radians and Arc Length: Solve problems related to radians and arc length, like finding an arc length given a central angle in radians and a radius.
  • Area of a sector: Relate the area of a sector to the area of the whole circle.  Aligns with C-B.5.

Performance tasks:

Illustrative Mathematics: Geometry: Setting up sprinklers: This task aligns with standards in C-B.

Mathematics Assessment Project: High School: Geometry: Task 441: Sectors of Circles

Mathematics Vision Project, Secondary 2 Student Edition:

 

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