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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CCSS.Math.Content.HSG-CO.C.10
congruence standard B7 high school common core

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congruence standards for high school common core
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Transformations

Define and perform rotations, reflections, dilations and translations.

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

mathematical definition of a line
what does dilation mean in math?
rigid motion

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

2 by 3 rectangle rotated 45 degrees
rotate (4, -3) 80 degrees clockwise
reflect the flag of Canada
rotate a picture of Barack Obama 44 degrees counterclockwise

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

90 degree rotation clockwise about (2,1)
reflect across y = x + 5
if f(x) = x^2, what is f(x) + 4
x + 1 vs (x + 1) + 6

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

rotate regular pentagon 360/5 degrees
reflect x^2 across x = 0
(5, 0) reflected across y = 0
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Triangles & Parallelograms

See relationships between measurements in geometric figures.

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

vertical angles
complementary angles
supplementary angles

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

triangle {{-7, 3}, {4, -9}, {1, 8}}
SAS 3 60deg 4
SSS 13 18 9
isosceles triangle edge lengths
{0, -5}, {1, 4}, {5, 2} triangle medians
{{1,1}, {3, 6}, {1, 8}} triangle incenter
7-8-9 triangle circumradius
triangle geometric properties

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

parallelogram width 4 and height 3
parallelogram with angles 30 deg and 150 deg
parallelogram side lengths 3, 5 angle 60 degrees
diagonals of parallelogram with sides 6 and 9 and angle 90 deg
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Geometric Constructions

Create visual arrangements of geometric objects.

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

line with slope 3/5 through point (1, 2)
line parallel to y = -4x + 9 through (0, -2)
perpendicular bisector of line between {1, 1} and {8, 3}
line perpendicular to 3x - 9
angle bisector

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

equilateral triangle inscribed in a circle
regular hexagon circumcircle
square inside a circle
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