Strategies for Solving Connection Problems

Instructor: Tawnya Eash

Tawnya has a master's degree in early childhood education and teaches all subjects at an elementary school.

Are you trying to figure out how to solve connection problems with polygons? Check out this lesson for a variety of strategies aimed at helping you connect two polygons with one line segment.

Spatial Skills

Being able to connect problems with polygons can greatly increase your spatial skills. Spacial skills allows you to use maps, orient yourself around your environment, and develop competent skills in your field of expertise. With them, a radiologist can read visual images portrayed through x-rays, an astronomer can visualize the solar system, and engineers can figure out how machines work.

Polygons are described as closed figures made up of three or more line segments. They cannot be open, have intersecting lines, or be made of curved lines.

Connecting Polygons

So how you can mentally attach two polygons with a line segment?

Begin with two polygons. By rotating these polygons around, you can attach them with a line segment.


Ways to Connect Polygons
Connect Polygons


Notice how the shapes stay the exact same, the point stays in the exact same location, and the connecting line is either vertical, horizontal, or could even be diagonal.

Solving Connection Problems

Using various strategies, in any order, can help you mentally rearrange polygons so that they can be connected with a line segment. It's important to make sure that you do nothing to change the original shapes or the location of the points on each shape. Let's go over the strategies in detail.

  1. Identify the location of each point

Make sure you note the location of each point in the original shapes. Points may be found on the vertex, inside a vertex, in the middle of the polygon, or on the inside of one of the line segments. They can be placed anywhere within the polygon, so as soon as you find the points, make sure your answer has them in the correct position.

  1. Rotate the polygons in your head

Another option is to rotate the images in your mind. Pretend you are grabbing your image and turning it with your hand. Turn it clockwise or counterclockwise. You could use the location of the point to help make sure you are rotating the shape correctly.

When rotating, remember to not change the shape or flip it. You are just moving it around in a circle so that the point is in a different position. This way, both shapes can be rotated so that the points line up to draw the line segment.

  1. Eliminate options

Say you are taking a multiple choice test. Eliminating choices you know are not correct helps you find the correct answer quicker and easier. Take a look at the possible solutions and get rid of the ones that make no sense. The answer is not correct if:

  • It shows a mirror image of the original polygon (a flip).
  • The point is in the wrong location.
  • The polygons are not the same as the original.

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