Domain 8.G, Geometry

Cluster 8.G.A, Understand congruence and similarity using physical models, transparencies, or geometry software.

Major Cluster

Standard 8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

30 Lessons

114 Activities

Standard 8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

21 Lessons

62 Activities

Standard 8.G.A.1.B

Angles are taken to angles of the same measure.

20 Lessons

58 Activities

Standard 8.G.A.1.C

Parallel lines are taken to parallel lines.

18 Lessons

51 Activities

Standard 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.

22 Lessons

89 Activities

Standard 8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

20 Lessons

66 Activities

Standard 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.

17 Lessons

101 Activities

Standard 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.

19 Lessons

90 Activities

Cluster 8.G.B, Understand and apply the Pythagorean Theorem.

Major Cluster

Standard 8.G.B.6

Explain a proof of the Pythagorean Theorem and its converse.

8 Lessons

32 Activities

Standard 8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

15 Lessons

54 Activities

Standard 8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

7 Lessons

25 Activities

Cluster 8.G.C, Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

Additional Cluster

Standard 8.G.C.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

19 Lessons

59 Activities