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Common Core High School Geometry Teaching and Learning Resources

Domain: SRT: Similarity, Right Triangles, and Trigonometry

Common Core Math

Select the cluster for resources on this page:

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SRT-A: Understand similarity in terms of similarity transformations

Standards:

 

Technology-enhanced investigations:

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

transformation dilation congruence tests for triangles area of a triangle
similar scale factor trig functions Law of Sines
similarity tests for triangles congruent SOHCAHTOA definitions Law of Cosines

 

LearnZillion:

National Library of Virtual Manipulatives: Dilations (Java required)

Southeast Comprehensive Center of SEDL: Video: Understand similarity in terms of similarity transformations: This video aligns with standard SRT-A.2.  View online or download.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 5 manipulatives addressing SRT-A.1, 16 manipulatives for STR-A.2, and 2 manipulatives for SRT-A.3.  Among those:

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: Similarity includes lessons, then practice problems on dilations, dilations and lines, similarity (numerical problems), similarity measurements, side splitter theorem, angle bisector theorem, and similarity proofs.  Use with SRT-A.1, SRT-A.2, SRT-A.3, SRT-B.4, and SRT-B.5.

MathsIsFun.com: Resizing: Dilation or resizing is defined and illustrated.  Learners then use a virtual manipulative to experiment with dilations involving a triangle, rectangle, and L-shape, selecting a scale factor and a center.  Following this experiment are multiple choice questions on resizing.  Aligns with SRT-A.1.

Constructed-response:

AlgebraLab.org: Similar 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: Practice questions with videos.

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

Performance tasks:

Illustrative Mathematics: Geometry:

Inside Mathematics: MARS Tasks:

Mathematics Assessment Project: High School: Geometry:

Mathematics Vision Project, Secondary 2 Student Edition:

 

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SRT-B: Prove theorems involving similarity

Standards:

 

Technology-enhanced investigations:

Cut the Knot: Pythagorean Theorem and its Many Proofs: Written proofs.

GeoGebra Book of Proofs Without Words for the Pythagorean Theorem by Steve Phelps is a series of manipulatives for exploration.

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.

Proofs of Pythagoras' Theorem Using Similarity: Aligns with SRT-B.4.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 10 manipulatives addressing SRT-B.4, 1 manipulative for STR-B.5.  Among those:

Multiple Choice:

Khan Academy: Practice questions with videos.

MathBitsNotebook: Geometry:

Constructed-response:

Khan Academy: Practice questions with videos.

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 in the classroom, and student activity sheet.  Aligns with CO-B.6, CO-C.9, SRT-B.5, and mathematical practice standards 1, 2, 3, and 7.

 

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SRT-C: Define trigonometric ratios and solve problems involving right triangles

Standards:

 

Technology-enhanced investigations:

right triangleAre you wondering why a2 + b2 = c2 in the right triangle?

Math is Fun includes an easy to understand Proof of the Pythagorean Theorem Using Algebra.  It uses the formulas for an area of a square and a triangle.

See the GeoGebra Book of Proofs Without Words for the Pythagorean Theorem by Steve Phelps, which is a series of manipulatives showing the proof in multiple ways.

Did you know that you don't need to just use squares on each side of the right triangle to illustrate the theorem

Try drawing semicircles with diameters a, b, and c on each side of the triangle to show a2 + b2 = c2.  Then see Pythagoras' Theorem and Areas at Math is Fun.  You can also use other "similar" geometric shapes (e.g., equilateral triangles drawn on each side).

GCSE Maths Tutor: Introducing Trigonometry: Videos 9-13 on Pythagorean theorem, sine, cosine, and tangent ratios for the right triangle, which align with SRT-C:

LearnZillion:

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: (Java required)

Ohio Resource Center on YouTube: Tutorials for High School Mathematics: Video 22: Right Triangle Trig.  A review of trig definitions and applying trig in practical problems.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 3 manipulatives addressing SRT-C.6, 1 manipulative for STR-C.7, and 7 manipulatives for STR-C.8.  Among those:

Multiple Choice:

CK-12: Geometry: Video examples, practice problems, and real world applications.  The following align with SRT-C.8:

MathBitsNotebook: Geometry:

Constructed-response:

AlgebraLab.org:  Lesson and fill in the blank practice problems.

Khan Academy: Right Triangles and Trigonometry unit. Practice questions with videos.

MATHguide.com: Pythagorean theorem quizmaster.  The following are fill in and check answers, which are rounded to the nearest tenth.  The formula is presented with the following:

Math.com: Pythagorean Theorem and Right Triangle: Lesson and fill-in the blank problems.

Performance tasks:

Illustrative Mathematics: Geometry:

Inside Mathematics: MARS Task: Hopewell Geometry: Students work with the Pythagorean theorem, find angles using trig ratios, and prove similarity involving triangles.  This task aligns with standards SRT-A.2, SRT-B.5, and SRT-C.6, SRT­C.7, SRT-C.8.

Mathematics Assessment Project: High School: Geometry:

Mathematics Vision Project, Secondary 2 Student Edition:

 

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SRT-D: Apply trigonometry to general triangles

Standards:

 

Technology-enhanced investigations:

CalculatorSoup:

Dave's Short Trig Course:

GCSE Maths Tutor: Introducing Trigonometry: Videos 14-16 align with SRT-D:

Khan Academy:

National Library of Virtual Manipulatives: Triangle Solver: Practice using Law of Sines and Law of Cosines.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 4 manipulatives addressing SRT-D.10, and 5 manipulatives for STR-D.11.  Among those:

Multiple Choice:

MathBitsNotebook: Geometry: Trigonometry: Oblique Triangles includes lessons, then practice problems on areas of triangles using trigonometry, law of sines, law of cosines, navigation and vectors.  Use with SRT-D.9, SRT-D.10, and SRT-D.11.

MathsIsFun.com: Tutorials on the Law of Sines and Law of Cosines.  Examples are shown.  Learners then complete 10 multiple choice problems on each law.  Aligns with SRT-D.10 and SRT-D.11.

Constructed-response:

Khan Academy: Non-right Triangles and Trigonometry unit. Practice questions with videos.

Performance tasks:

Georgia Standards of Excellence Framework: Pre-Calculus Unit 3: Trigonometry of General Triangles.  This unit contains five tasks: Finding a New Area Formula for Triangles, Proving the Law of Cosines, Proving the Law of Sines, The Hinge Theorem, and a Culminating Task: Combining Lots.  Tasks align to SRT-D.9, SRT-D.10, SRT-D.11, and are also related to SRT-C.6, SRT-C.7, and SRT-C.8.

Mathematics Vision Project, Secondary 3 Student Edition:

 

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