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Common Core High School Geometry Teaching and Learning Resources

Domain: CO: Congruence

Common Core Math

Select the cluster for resources on this page:

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CO-A: Experiment with transformations in the plane

Standards:

 

Technology-enhanced investigations:

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

Angle Alternate Interior Angles Congruent Rectangle
Altitude Corresponding Vertical Angles Square
Angle Bisector Transformation
Median of a Triangle Point
Circle Triangle Congruence Diagonal of a Polygon Rhombus
Arc of a Circle Parallelogram Dilation Trapezoid
Line Perpendicular Rotation Equilateral Triangle
Parallel Lines Line Segment Reflection Isosceles Triangle
Transversal Midpoint Translation Regular Polygon
Alternate Exterior Angles Perpendicular Bisector Theorem  

 

Imagine Learning Classroom (formerly LearnZillion) subscription needed: Lesson set: Define geometric terms precisely: Four video lessons: Definitions and representations are distinct, understand the importance of precise definitions, why point and line are undefinable; and define geometric terms precisely.  Aligns with CO-A.1.

Math.com: Quadrilaterals: Students learn about the five most common quadrilaterals: parallelogram, square, rectangle, rhombus, trapezoid.  Use with CO-A.3.

Mathwords.com: Index for Geometry: Terms from plane and solid geometry.  This interactive math dictionary has words, terms, formulas, pictures, diagrams, tables, and examples.  Use with CO-A.

Mathbits.com: Use with CO-A.2.

Mathematical Association of America Mathematical Sciences Digital Library: Loci Resources: Using GeoGebra and Exploring Geometric Transformations in a Dynamic Environment: There are eight activities, which address reflections, rotations, translations, glide-reflections, and reflections with parallel lines, intersecting lines, and concurrent lines.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  The Pythagorean Theorem: Geometry's Most Elegant Theorem: "This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications."  Aligns with CO-A.1 and SRT-C.6, SRT-C.8.

National Library of Virtual Manipulatives: Transformations (Java required for online use)

Shodor Interactivate:

Walter Fendt's Sum of Angles in a Triangle, Virtual Manipulative

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 1 manipulative for CO-A.1, 29 manipulatives for CO-A.2, 14 manipulatives for CO-A.3, 43 manipulatives for CO-A.4, 105 manipulatives for CO-A.5. Among those:

YouTube video lessons:  Use the following with CO-A.1:

 

Multiple Choice:

CK-12: Dilations in the Coordinate Plane: Practice questions with review content and video.  Review content includes a Types of Transformations Study Guide, which is an overview of reflection, rotation, dilation, and translation.   Aligns with CO-A.2 and SRT-A.1.

Khan Academy: Practice questions with videos.

MathBitsNotebook: Geometry:

MathsIsFun.com: Transformations: Learners use virtual manipulatives to experiment with rotations, reflections, and translations of a triangle, rectangle, or L-shape, setting parameters for each experiment.  Following each section are multiple choice questions.  Aligns with CO-A.5.

Constructed-response:

Khan Academy: HSG-G-CO includes HSG-CO.A.1 through HSG-CO.A.5 Common Core aligned problems.

Also see Performing transformations: unit on translations, rotations, reflections, dilations. Practice questions with videos.

Performance tasks:

Illustrative Mathematics: Geometry:

Mathematics Vision Project, Secondary 1 Student Edition: Module 6: Congruence, Construction, and Proof: This module contains 14 classroom tasks.  Geometry standards addressed in Module 5 include CO-A.1, CO-A.2, CO-A.3, CO-A.4, CO-A.5 and CO-B.6, CO-B.7, CO-B.8, and CO-D.12, CO-D.13, and GPE-B.5.  Choose the following within the module: 

NCTM's Reasoning and Sense Making Task Library: Taking a Spin includes the task overview, teacher notes for its use, and student activity sheet.  Aligns with CO-A.3, CO-A.4 and mathematical practice standards 3 and 8.

 

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CO-B: Understand congruence in terms of rigid motions

Standards:

 

Technology-enhanced investigations:

Math Open Reference: Congruent Triangles: Investigate the theorems for congruence.

National Library of Virtual Manipulatives: investigate methods for determining congruent triangles (Java required). Explore SSS, SAS, ASA, SSA.  Note SSA does not guarantee congruent triangles.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 32 manipulatives for CO-B.6. Among those:

Multiple Choice:

Khan Academy: Practice questions with videos.

MathBitsNotebook: Geometry:

Constructed-response:

AlgebraLab.org: Congruent Triangles: Lesson and fill in the blank practice problems, including word problems.  Be sure to show the related AlgebraLab documents for additional practice problems.

Khan Academy: HSG-G-CO includes HSG-CO.B.6 through HSG-CO.B.8 Common Core aligned problems.

Also see the following practice questions with videos.

Math.com: Congruent Figures: Lesson and fill-in the blank matching problems.

Performance tasks:

Illustrative Mathematics: Geometry:

Mathematics Assessment Project: High School: Geometry: Task 452: Analyzing Congruence Proofs

Mathematics Vision Project, Secondary 1 Student Edition: Module 6: Congruence, Construction, and Proof: This module contains 14 classroom tasks.  Geometry standards addressed in Module 5 include CO-A.1, CO-A.2, CO-A.3, CO-A.4, CO-A.5 and CO-B.6, CO-B.7, CO-B.8, and CO-D.12, CO-D.13, and GPE-B.5. Task 5: Symmetries of Quadrilaterals; Task 6: Symmetries of Regular Polygons; and Task 7: Quadrilaterals-Beyond Definition align with standard CO-B.6.  Task 9: Congruent Triangles aligns with standards CO-B.6, CO-B.7, CO-B.8.

NCTM's Reasoning and Sense Making Task Library: Bank Shot includes the task overview, teacher notes for its use, and student activity sheet.  Aligns with CO-B.6, CO-C.9, SRT-B.5, and mathematical practice standards 1, 2, 3, and 7.

New York City School System: High School Geometry: Company Logo: Unit Overview: “This 3-4 week unit uses an investigation of rigid motions and geometric theorems to teach students how to verify congruence of plane figures and use the implications of congruence to solve problems and create proofs about geometric relationships. Students will demonstrate mastery of the content by making sense of the Company Logo Performance Task and persevering in solving the task.” Geometry standards addressed include CO-B.6, CO-B.7, CO-C.9, CO-C.10, and SRT-B.5.  Mathematical Practices standards include MP.1, MP.3, and MP.6.

 

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CO-C: Prove geometric theorems

Standards:

 

Technology-enhanced investigations:

Imagine Learning Classroom (formerly LearnZillion) subscription needed: Lesson set: Prove theorems concerning triangles and parallelograms: Six video lessons: Use triangle congruence (SAS), use triangle similarity to prove Triangle Midsection Theorem and Concurrency of Medians Theorem, use parallel lines and triangle congruence theorems to prove properties of parallelograms, including properties of diagonals of parallelograms, use properties of parallelograms and triangles to solve a real-world problem.  Aligns with CO-C.10 and CO-C.11.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary. The Broken Stick Experiment: Triangles, Random Numbers and Probability: "In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities."  Aligns with CO-C.10.

Saltire Software: Geometry Applet Gallery contains some excellent applets, which are easy to use and suitable for exploring several geometry theorems. Select from the following:

Shodor Interactivate: Angles: This lesson addresses acute, obtuse, and right angles as well as relationships between angles formed by parallel lines crossed by a transversal, including vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, same-side interior angles, same-side exterior angles, and corresponding angles.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 1 manipulative for CO-C.9, 15 manipulatives for CO-C.10, 2 manipulatives for CO-C-11. Among those:

YouTube Videos:

Multiple Choice:

Khan Academy: Practice questions with videos.

Shodor Interactivate: Angles: This applet with drop-down choices for responses provides an interactive quiz for learners to practice their knowledge of acute, obtuse, and alternate angles. Also, practice relationships between vertical, adjacent, alternate, same-side, and corresponding angles.  Learners can use either one or two transversals crossing parallel lines.

National Library of Virtual Manipulatives: walk through a visual proof of the Pythagorean theorem.

Constructed-response:

AlgebraLab.org:  Lesson and fill in the blank practice problems.  Be sure to show the related AlgebraLab documents for additional practice problems on each topic.

Khan Academy: HSG-G-CO includes HSG-CO.C.9 through HSG-CO.C.11 Common Core aligned problems.

Also see the following practice questions with videos.

Math.com: Angles and Intersecting Lines: Lesson and fill-in the blank matching problems.

MathBitsNotebook: Geometry:

Performance tasks:

Illustrative Mathematics: Geometry:

Inside Mathematics: MARS Tasks:

Mathematics Assessment Project: High School: Geometry:

Mathematics Vision Project, Secondary 2 Student Edition:

NCTM's Reasoning and Sense Making Task Library: Bank Shot includes the task overview, teacher notes for its use, and student activity sheet.  Aligns with CO-B.6, CO-C.9, SRT-B.5, and mathematical practice standards 1, 2, 3, and 7.

New York City School System: High School Geometry: Company Logo: Unit Overview: “This 3-4 week unit uses an investigation of rigid motions and geometric theorems to teach students how to verify congruence of plane figures and use the implications of congruence to solve problems and create proofs about geometric relationships. Students will demonstrate mastery of the content by making sense of the Company Logo Performance Task and persevering in solving the task.” Geometry standards addressed include CO-B.6, CO-B.7, CO-C.9, CO-C.10, and SRT-B.5.  Mathematical Practices standards include MP.1, MP.3, and MP.6.

 

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CO-D: Make geometric constructions

Standards:

 

Technology-enhanced investigations:

Desmos: Geometry Tool

GeoGebra: free open-source software

Khan Academy: Geometric Constructions unit includes tutorial videos on the following:

MathsIsFun.com: Constructions: This is an excellent series of 17 animated geometric constructions, which learners would do with a compass, pencil, and straightedge only.  They demonstrate how to construct a perpendicular bisector, angle bisector, 30-45-60 degree angles and equilateral triangle, perpendicular line to a line from a point on or off the line, parallel lines, congruent angles, a line cut into "n" pieces.  Circle constructions include 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 CO-D.12 and CO-D.13.

Math Open Reference: Constructions: The site provides step-by-step animations of constructions with compass and straightedge.  The Table of Contents for the Constructions is comprehensive for lines, line segments, angles, triangles, circles, arcs, ellipses, polygons, and non-Euclidean constructions.  Aligns with CO-D.12 and CO-D.13.

Robo Compass is an online app for geometric constructions, transformations, patterns and tesselations.  It works "exactly as you do using a physical straightedge, compass and protractor."  Documentation is included.

Whistler Alley Mathematics: Geometry Construction Reference: This includes illustrations and steps for geometric constructions.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 20 manipulatives for CO-D.12, 3 manipulatives for CO-D.13. Among those:

Multiple Choice:

Khan Academy: HSG-G-CO includes HSG-CO.D.12 Common Core aligned problems.

MathBitsNotebook: Geometry: Constructions and Concurrencies includes lessons on how to construct with compass and straightedge and other tools (e.g., a reflective edge, string, paper-folding, and dynamic geometric software), points of concurrency, and locus theorems.  Practice problem are on basic and more constructions, using constructions, constructions and reflections, points on concurrency, and locus.  Use with CO-C.10, CO-D.12 and CO-D.13.

Constructed-response:

 

Performance tasks:

Illustrative Mathematics: Geometry:

Mathematics Assessment Project: High School: Geometry: Task 403: Inscribing and Circumscribing Right Triangles

Mathematics Vision Project, Secondary 1 Student Edition: Module 6: Congruence, Construction, and Proof: This module contains 14 classroom tasks.  Geometry standards addressed in Module 5 include CO-A.1, CO-A.2, CO-A.3, CO-A.4, CO-A.5 and CO-B.6, CO-B.7, CO-B.8, and CO-D.12, CO-D.13, and GPE-B.5. Task 11: Under Construction; Task 12: More Under Construction; Task 13: Justifying Construction; and Task 14: Construction Blueprints align with standards CO-D.12 and CO-D.13.

 

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