Examples for

Common Core Math: High School Geometry

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.

Congruence

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

Visualize transformations (CCSS.Math.Content.HSG-CO.A.2):

Draw geometric objects (CCSS.Math.Content.HSG-CO.D.12):

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Circles

Get equations and properties of circles.

Compute arc lengths and sector areas (CCSS.Math.Content.HSG-C.B.5):

Inscribe circles within polygons (CCSS.Math.Content.HSG-C.A.3):

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Modeling with Geometry

Connect geometry with measurements in the physical world.

Compute density in various contexts (CCSS.Math.Content.HSG-MG.A.2):

Use geometry to solve design problems (CCSS.Math.Content.HSG-MG.A.3):

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Similarity & Trigonometry

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

Solve for unknown measurements in right triangles (CCSS.Math.Content.HSG-SRT.C.8):

Apply the laws of sines and cosines (CCSS.Math.Content.HSG-SRT.D.11):

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Expressing Geometric Properties with Equations

Use algebraic notation to describe geometric figures.

Identify circles with equations (CCSS.Math.Content.HSG-GPE.A.1):

Determine a parabola in terms of its focus and directrix (CCSS.Math.Content.HSG-GPE.A.2):

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