Examples for

In high school, students learn about geometric figures with particular emphases on triangles and circles. Students use relationships between the sides and angles of triangles to compute the trigonometric ratios sine, cosine and tangent. Students express circles (and, in advanced classes, parabolas, ellipses and hyperbolas) using algebraic equations and use angles to compute arc lengths and sector areas. Another key geometric concept is transformations of figures in the coordinate plane; students rotate, reflect, translate and dilate figures and explore how knowledge of these transformations can lead to definitions of similarity and congruence. Students learn a variety of theorems that can be applied to prove that two shapes are similar or congruent. Students also work with three-dimensional solids, computing their volumes and visualizing their cross sections, including in physical-world contexts.

Define and visualize what it means for geometric figures to be congruent.

Get equations and properties of circles.

Connect geometry with measurements in the physical world.

Analyze lengths and angles in geometric figures, including using trigonometric ratios.

Use algebraic notation to describe geometric figures.

Compute volumes and visualize cross sections of geometric solids.