Critical Thinking: Analyze and apply geometric relationships within triangles to solve complex problems.
Communication: Effectively articulate and present findings on the properties of triangles and their applications.
Global Citizenship: Recognize and explore the role of geometric principles in addressing global challenges and innovations.
How do the properties of triangle congruence and similarity influence our understanding of geometric figures?
In what ways do special points within a triangle (centroid, circumcenter, incenter, and orthocenter) reveal about its properties and potential applications?
How can understanding the relationships within triangles enhance problem-solving in real-world contexts, such as in engineering and architecture?
Students are able to convert quantitative problems that use words into mathematical expressions.
CCSS.MATH.CONTENT.HSG.CO.A.5: Theorems about triangles; the student understands 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.MATH.CONTENT.HSG.SRT.D.9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
CCSS.MATH.CONTENT.HSG.MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost).
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