Note: Click any standard to move it to the center of the map.
[6.G.A.3] -
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
Mathematics | Grade : 8
Domain - Geometry
Cluster - Understand congruence and similarity using physical models, transparencies, or geometry software.
[8.G.A.3] - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- Dilation
A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor. - Reflection
A type of transformation that flips points about a line, called the line of reflection. Taken together, the image and the pre-image have the line of reflection as a line of symmetry. - Rotation
A type of transformation that turns a figure about a fixed point, called the center of rotation. - Translation
A type of transformation that moves every point in a graph or geometric figure by the same distance in the same direction without a change in orientation or size.
[8.G.A.1] -
Verify experimentally the properties of rotations, reflections, and translations.
[8.G.A.4] -
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
[GEO.G-CO.A.5] -
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
[GEO.G-SRT.A.1.a] -
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
[GEO.G-SRT.A.1.b] -
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
[GEO.G-GPE.B.4] -
Use coordinates to prove simple geometric theorems algebraically, including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
[MI.G-CO.A.5] -
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
[MII.G-SRT.A.1.a] -
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
[MII.G-SRT.A.1.b] -
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
[MII.G-GPE.B.4] -
Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).