Geometry Problems and Investigations

Here are several geometry problems and investigations. The geometry content of these pages target the high school level. It is possible that students of other levels will be successful, too!

Broken Plate Problem: You have found part of plate and the design looks like a rare plate. If you can determine the diameter of the plate, then you will know if it the rare plate or just a copy.

Angle Sum Problem: Try to find a triangle which the sum of any two angles, no matter which two you pick, is less than 120°.

Triangle Dilation Investigation: Is it possible for similar figures to be congruent?

Acute Triangle Problem: What is the least number of (smaller) acute-angled triangles you can dissect each of these triangles into?

Intersecting Boat Docks: In a circular lake (size doesn´t matter), there are two boat docks (chords), AB and CD, intersect at point X.AB has a length of 7 m, and the point X divides it so that AX = 3 m.

Distribution Center Problem: You deliver goods to three cities (Apple, Bat, Cat). You are going to build a distribution center and want it to be equal distant from each city. Where are you going to place it?

Rotation of Chords & Line Segments:

Football Field Problem:

River’s Width Problem: Use similar triangles to determine the width of a river.

Square Root of 3: Prove the axes of a figure have a ratio of 1 to the square root of 3.