# 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