Big Ideas Geometry Chapters 5-6
November – December (5 weeks); 1st Semester
Big Ideas Geometry Chapters 5-6
November – December (5 weeks); 1st Semester
Chapter Title(s):
Congruent Triangles (Chapter 5)
Relationships Within Triangles (Chapter 6)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
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-CO.B. Congruence: Understand congruence in terms of rigid motions.
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. (CCSS: HS.G-CO.B.7)
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (CCSS: HS.G-CO.B.8)
HS.G-CO.C. Congruence: Prove geometric theorems.
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. (CCSS: HS.G-CO.C.10)
HS.G-SRT.B. Similarity, Right Triangles, and Trigonometry: Prove theorems involving similarity.
Use congruence criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS: HS.G-SRT.B.5)
HS.G-C.A. Circles: Understand and apply theorems about circles.
Construct the inscribed and circumscribed circles of a triangle. (CCSS: HS.G-C.A.3)
HS.G-GPE.B. Expressing Geometric Properties with Equations: Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically. (CCSS: HS.G-GPE.B.4)
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:
Establish facts about the angle sum of triangles and angles created when parallel lines are cut by a transversal (Grade 8)
Academic Vocabulary & Language Expectations:
Interior angles, exterior angles, corollary to a theorem, corresponding part, legs, vertex angle, base, base angles, hypotenuse, coordinate proof, equidistant, concurrent, point of concurrency, circumcenter, incenter, median of a triangle, centroid, altitude of a triangle, orthocenter
Assessments:
SAT Suite Educator Question Bank (Content Domain: Geometry and Trigonometry)
Instructional Resources & Notes:
Big Ideas Geometry Chapters 5-6 (skip Lessons 6.4, 6.6)
Additional Modeling Tasks
Calling All Islanders (References: Completing the Modeling Cycle, Advice on Modeling)
Notes:
Students do not need to construct points of concurrency (circumcenter, incenter, centroid, orthocenter) independently or know their properties; these constructions can be limited to in-class activities.
Lesson 6.4 (The Triangle Midsegment Theorem) is optional and can be reserved for Honors Geometry classes only.
In Lesson 6.5 (Indirect Proof and Inequalities in One Triangle), focus on the "Triangle Longer Side Theorem" and "Triangle Larger Angle Theorem" only.
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:
HS.G-CO.D. Congruence: Make geometric constructions.
(+) Construct an equilateral triangle and a regular hexagon inscribed in a circle. (CCSS: HS.G-CO.D.13)
Lesson 6.4: The Triangle Midsegment Theorem
Lesson 6.5: Indirect Proof and Inequalities in One Triangle (additional theorems)
Lesson 6.6: Inequalities in Two Triangles