Big Ideas Geometry Chapter 9
February – March (3 weeks); 2nd Semester
Embedded Files
Chapter Title(s):
Right Triangles and Trigonometry (Chapter 9)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP4. Model with mathematics.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
4. Geometry
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
HS.G-SRT.B. Similarity, Right Triangles, and Trigonometry: Prove theorems involving similarity.
Prove theorems about triangles. Theorems include: the Pythagorean Theorem proved using triangle similarity. (CCSS: HS.G-SRT.B.4)
HS.G-SRT.C. Similarity, Right Triangles, and Trigonometry: Define trigonometric ratios and solve problems involving right triangles.
Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (CCSS: HS.G-SRT.C.6)
Explain and use the relationship between the sine and cosine of complementary angles. (CCSS: HS.G-SRT.C.7)
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.⭑ (CCSS: HS.G-SRT.C.8)
A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.
Additional Colorado Academic Standards Resources:
Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:
Colorado Essential Skills and Mathematical Practices connections
Inquiry Questions
Coherence Connections
Prior Knowledge Connections:
Using the Pythagorean Theorem (Grade 8)
Academic Vocabulary & Language Expectations:
Pythagorean Theorem, Pythagorean triple, special right triangles, trigonometric ratio, tangent, angle of elevation, sine, cosine, angle of depression, angle of elevation, inverse tangent, inverse sine, inverse cosine, solve a right triangle
Assessments:
SAT Suite Educator Question Bank (Content Domain: Geometry and Trigonometry)
Instructional Resources & Notes:
Big Ideas Geometry Chapter 9 (skip Lessons 9.3, 9.7)
Additional Modeling Tasks
Algebra 1 Review:
In addition to the Review & Refresh exercises included with each Big Ideas Geometry lesson, the following resources can be used for curating frequent, ongoing mixed review exercise sets of key Algebra 1 concepts and skills. These resources focus on linear equations, linear functions, systems of equations & inequalities, exponential functions, quadratic functions, and quadratic equations:
Algebra Warm-Ups for Geometry Teachers (Geoff Krall)
SAT Suite Educator Question Bank (Content Domains: Algebra, Advanced Math)
Honors Geometry:
Honors Geometry students can extend their learning beyond the Colorado Academic Standards with the following concepts and lessons:
Lesson 9.3: Similar Right Triangles
Lesson 9.7: Law of Sines and Law of Cosines
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