Examples for

Common Core Math: High School Geometry: Congruence

In high school, students identify and perform transformations of two-dimensional figures in the coordinate plane. In particular, students distinguish the class of transformations known as "rigid motions," which preserve the measurements of a transformed figure. Students use rigid motions to define congruence: two figures are congruent if one can be mapped directly onto the other with a series of rigid motion transformations. Students use the idea of congruence to prove facts about the measurements of triangles, parallelograms and other geometric figures. Students also use knowledge of geometric relations to sketch geometric objects, including bisecting angles and inscribing polygons in circles.

Common Core Standards

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Triangles & Parallelograms

See relationships between measurements in geometric figures.

Describe related angles (CCSS.Math.Content.HSG-CO.C.9):

Explore measurements of triangles (CCSS.Math.Content.HSG-CO.C.10):

Explore measurements of parallelograms (CCSS.Math.Content.HSG-CO.C.11):


Define and perform rotations, reflections, dilations and translations.

Get definitions of geometric objects (CCSS.Math.Content.HSG-CO.A.1):

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

Represent and describe transformations (CCSS.Math.Content.HSG-CO.A.2):

Identify transformations that carry a figure onto itself (CCSS.Math.Content.HSG-CO.A.3):

Geometric Constructions

Create visual arrangements of geometric objects.

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

Inscribe polygons in circles (CCSS.Math.Content.HSG-CO.D.13):