Geometry

Eighth grade is where geometry stops being a parade of vocabulary and starts asking students to do something. Figures move on the coordinate plane. Similar triangles get checked with numbers. The Pythagorean Theorem stops being a thing kids memorized in seventh grade and becomes a tool they reach for half a dozen times a week. These worksheets walk through that whole arc — nine weeks of standards-aligned practice with concept passages and worked examples built in, so kids aren’t staring at a problem set wondering what the symbols mean.

The first three weeks live on the coordinate plane. Week 1 introduces the three rigid motions — translations, rotations, and reflections — and the idea that congruence is what happens when one figure can be carried onto another by a sequence of those motions. Week 2 drills the rotation rules about the origin (90°, 180°, and 270° counterclockwise) until the coordinate substitutions feel automatic. Week 3 widens out to the full set of transformation rules — reflections across both axes and the line y=x, combined with translations and rotations — and uses them to verify congruence.

Week 4 introduces dilations and similarity, and this is the week the unit’s vocabulary really shifts. Figures can now change size. Scale factor matters. Two figures are similar if one is the dilation-plus-rigid-motion image of the other, and that’s verified by checking corresponding sides for proportionality. Week 5 steps off the coordinate plane briefly to handle the classical angle work — parallel lines cut by a transversal, the eight angle pairs that arrangement creates, the triangle angle sum theorem, and the exterior angle theorem.

Then the unit pivots to the Pythagorean Theorem and stays there for two weeks. Week 6 develops both the statement (a² + b² = c²) and a visual area-of-squares proof, then applies the theorem to find missing legs and hypotenuses and uses the converse to test whether three side lengths form a right triangle. Week 7 takes that same theorem into the real world — ladders, diagonals across rectangular fields, indirect measurement — and derives the distance formula by treating two points on a coordinate plane as the endpoints of a right triangle’s hypotenuse.

Week 8 turns to volume of curved solids: cylinders (πr²h), cones (⅓πr²h), and spheres (4⁄3πr³). Worksheets compare solids that share dimensions, solve real-world container problems, and work backward from a known volume to find a missing radius or height. Week 9 is a capstone — five worksheets that mix every major concept from the unit into multi-step problems and original designs, so students leave the year integrating transformations, similarity, angle relationships, the Pythagorean Theorem, the distance formula, and volume rather than treating them as separate chapters.

Every week includes five worksheets and full answer keys. The content is Common Core aligned to 8.G.A.1 through 8.G.C.9 and works equally well as a primary homeschool sequence, a tutoring spine, or a summer review before high school geometry.