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Mathematics > Grade 8 > Geometry
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Mathematics | Grade : 8

Domain - Geometry

Cluster - Understand congruence and similarity using physical models, transparencies, or geometry software.

[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.

Resources:


  • 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.
  • Sequence, progression
    A set of elements ordered so that they can be labeled with consecutive positive integers starting with 1, e.g., 1, 3, 9, 27, 81. In this sequence, 1 is the first term, 3 is the second term, 9 is the third term, and so on.
  • Similarity transformation
    A rigid motion followed by a dilation.
  • 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.
  • Ambassador Task: Car Logos

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

  • GEO.G-CO.A.3
    Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • GEO.G-SRT.A.2
    Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • GEO.G-C.A.1
    Prove that all circles are similar.
  • MI.G-CO.A.3
    Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • MII.G-SRT.A.2
    Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • MII.G-C.A.1
    Prove that all circles are similar.

Same Level Standards:

  • 8.G.A.2
    Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  • 8.G.A.3
    Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • 8.G.A.5
    Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.