8th Grade Geometry: What Students Should Know

In 8th grade, students are preparing for the more challenging math curriculum of high school. Keep reading to find out what your 8th grader will be expected to learn and how you can help him or her prepare.

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What Students Learn in 8th Grade Geometry

Translations, Reflections and Rotations

In geometry, 8th graders translate, reflect and rotate 2-dimensional shapes. To translate a shape, you slide the shape to another spot on a coordinate plane. To reflect a shape, you flip it. Essentially, the shapes are mirror images of one another.

Finally, when a shape is rotated, it pivots on one spot, so it points in a different direction than the original shape. Students must also determine whether shapes are congruent (identical), even if they are translated, reflected or rotated.

To practice these skills at home, draw a shape, like a triangle, on a graph. Then, ask your child to translate the shape five spaces to the right, reflect the translation to the left and rotate the shape 180 degrees. Alternatively, rotate, reflect and translate a shape yourself and ask your 8th grader to decide if it is congruent with the original shape.

Pythagorean Theorem

The Pythagorean Theorem is used to identify an unknown length of a right triangle. The formula is a^2 + b^2 = c^2, where c represents a triangle's hypotenuse and a and b represent its other two sides. Your 8th grader may also use the Pythagorean Theorem to calculate the distance between two points on a coordinate plane.

To practice this at home, your 8th grader can calculate distances in the real world. For this activity, you will need to plan an imaginary road trip. Begin by creating a right triangle using three points on the map. Measure the distance in miles for two of the sides. Then, ask your child to calculate the third unknown distance using the Pythagorean Theorem.


Students in 8th grade learn the formulas to calculate the volume for cones, cylinders and spheres. Then, they use these formulas to solve real-world problems. For instance, students may calculate how many gallons of water are needed to fill a circular pool that is five feet tall and six feet in diameter. The formula is V = pi (r^2) h, where pi equals 3.14, r is the radius and h is the height. So, for a pool that is five feet tall and has a radius of three (half of six), the volume would be 141.3 cubic feet.

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