Math for Middle Schoolers: Geometry

Learn to identify four types of angles—right, acute, obtuse, and straight—using their measures: 90 degrees, less than 90 degrees, greater than 90 degrees, and 180 degrees.

Learn to identify and label perpendicular lines that form 90-degree angles and to identify and label parallel lines, which never intersect and share the same direction using arrows.

Learn how complementary angles sum to 90 degrees and supplementary angles sum to 180, and use these ideas to find unknown angle measures in triangles and lines.

explore vertical, corresponding, and alternate interior angles formed by a transversal across parallel lines, and learn to solve for x, y, and z using their relationships.

Explore squares as equal-sided quadrilaterals with right angles, parallel and perpendicular sides, and equal diagonals, then apply the perimeter 4x and area x^2 formulas with examples.

Explore rectangles as a quadrilateral with right angles, equal opposite sides, and parallel pairs; apply the perimeter formula 2(x+y) and area x*y, with example calculations.

Learn how parallelograms have opposite sides equal and parallel, opposite angles equal, and how to find their perimeter using 2(x+y) and area using base times height, with examples.

Learn about trapezoids, a quadrilateral with parallel bases, equal opposite angles, and equal diagonals; compute perimeter with x + 2y + z and area with 1/2 h (x+z).

Explore the cylinder’s parts, define radius and height, and apply the surface area and volume formulas (2πr^2+2πrh and πr^2h) with example calculations.

Explore pyramids and cones in geometry by calculating volumes using base area and height, with formulas for square, rectangle, triangle bases, and pi r^2 h for cones.

Explore spheres as 3-D figures with no faces or edges, and apply surface area and volume formulas 4 pi r^2 and 4/3 pi r^3 through worked examples involving radii.

Explore triangles as a 2d shape with three sides and angles, learn that interior angles sum to 180 degrees, and apply area formula using base and height, including exterior angles.

Identify isosceles triangles by equal sides and angles. Equilateral have all sides equal, 60-degree angles; scalene have different sides and angles; right triangles have a right angle and a hypotenuse.

Use the Pythagorean theorem to determine a missing side in a right triangle, applying c^2 = a^2 + b^2 with given legs or hypotenuse.

Explore how pythagorean triples satisfy the pythagorean theorem in right triangles, and learn to recognize and use 3-4-5, 5-12-13, 7-24-25, 8-15-17, 9-40-41, and their multiples to quickly find the hypotenuse.

Explore similarity in triangles by comparing equal corresponding angles and proportional sides, determine scale factors, and identify when figures are not similar using side ratios and angle checks.

Explore the next steps in middle school geometry and discover related courses in algebra, statistics, and French to expand your knowledge.