Geometry: Concepts and Connections

Mathematical Practices

Mathematical Modeling 

Patterning & Algebraic Reasoning

Geometric & Spatial Reasoning 

Probabilistic Reasoning

Data & Statistical Reasoning 

Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.

Apply mathematics to real-life situations; model real-life phenomena using mathematics.

Interpret the structure of polynomial expressions and perform operations with polynomials within a geometric framework.

Experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain real-life phenomena.

Establish facts between angle relations and generate valid arguments to defend facts established. Prove theorems and solve geometric problems involving lines and angles to model and explain real-life phenomena.

Describe dilations in terms of center and scale factor and use these terms to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion for triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain real-life phenomena.

Examine side ratios of similar triangles; use the relationship between right triangles to develop an understanding of sine and cosine to solve geometric problems and to model and explain real-life phenomena.

Explore the concept of a radian measure and special right triangles.

Examine and apply theorems involving circles; describe and derive arc length and area of a sector; and model and explain real-life situations involving circles.

Develop informal arguments for geometric formulas using dissection arguments, limit arguments, and Cavalieri’s principle; solve realistic problems involving volume; explore and visualize relationships between two-dimensional and three-dimensional objects to model and explain real-life phenomena.

Solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions.

Examine real-life situations presented in a two-way frequency table to calculate probabilities, to model categorical data, and to explain real-life phenomena.