Here is my summary of what all middle school students are expected to learn about Geometry by the end of eighth grade, based on the Common Core state standards in math for sixth, seventh, and eighth grades. (Note: "e.g." means "for example".)

### I. Area, perimeter, circumference, surface area, and volume

- Know and use formulas for
area of triangles, rectangles, parallelograms, and two-dimensional shapes
made from these (6.G.1), and circle area and circumference (7.G.4).
- Know and use formulas for
the volumes of right rectangular prisms (boxes) with fractional edge
lengths (6.G.2), three-dimensional objects composed of cubes and right
prisms (7.G.6), and cones, cylinders, and spheres (8.G.9).
- Find the surface area of
two- and three-dimensional objects composed of triangles, quadrilaterals,
polygons, cubes, and right prisms. (7.G.6)
- Represent 3-D figures with
nets, and use nets to find surface area. (6.G.4)
- Describe what 2-D shapes you would get by slicing 3-D objects like boxes, cylinders or pyramids. (7.G.3)

### II. Scale and Similarity

- Interpret scale drawings,
and reproduce scale drawings with a different scale. (7.G.1)
- Draw (freehand, with ruler
and protractor, and with technology) geometric shapes with given
conditions (e.g. triangles with certain angle measures and side lengths).
(7.G.2)
- Recognize what conditions
(e.g. combinations of side lengths or angles) determine a unique triangle,
more than one triangle, or no triangle. (7.G.2)
- Use informal arguments to
establish facts about the angle-angle criterion for similarity of
triangles. (8.G.5)

### III. Angles

- Use facts about
supplementary, complementary, vertical, and adjacent angles in a
multi-step problem to write and solve simple equations for an unknown
angle in a figure. (7.G.5)
- Use informal arguments to
establish facts about the angle sum and exterior angle of triangles.
(8.G.5)
- Use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. (8.G.5)

### IV. Transformations

- Rotations, reflections, and translations: know side lengths & angle measures are preserved, and parallel lines are still parallel. (8.G.1)
- Describe how to get one
congruent or similar figure from another with transformation(s). (8.G.2
and 8.G.4)
- Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (8.G.3)

### V. The Pythagorean Theorem

- Explain a proof of the
Pythagorean Theorem and its converse. (8.G.6)
- Apply the Pythagorean
Theorem to determine unknown side lengths in right triangles in two and
three dimensions. (8.G.7)
- Apply the Pythagorean
Theorem to find the distance between two points in a coordinate system.
(8.G.8)

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