What Are Some Hard Geometry Problems?

What Are Some Hard Geometry Problems?

The National Council of Teachers of Mathematics has published guidelines for geometry that should be mastered at each grade level. However, whether the geometry problems are hard to solve depends on each student's ability.

In preschool, students are expected to understand distance and direction, and be able to identify geometric shapes in two and three dimensions on paper and in the real world.

Grade school students learn to identify more complex shapes, calculate volume and area, learn basic coordinate systems and calculate the distance between points.

Middle and high school students learn about Cartesian coordinates, polygons, function notation, conjectures, theorems, translations, reflections and dilations of objects, and they are introduced to trigonometry.

Math.com has geometry practice problems that include transformation, fractal, congruent triangle, tesselation and Pythagorean theorem problems. Additionally, the site has tables of formulas for surface area, volume, polygons, perimeters and circles.

AnalyzeMath.com has geometry tutorials that cover inscribed and central angles in circles, parallel lines and angles, polygons, rotation symmetry and formulas to determine the volumes of spheres, cones and cylinders.

IXL.com has a detailed page with interactive geometry practice problems that range from simple midpoint problems to geometric probability questions.

Additional sources of geometry practice problems can be found in math textbooks generally following the texts' appendices.