How To Solve Geometric Problems

How To Solve Geometric Problems-43
Use this step to fill in as much missing information in your diagram as you can.At this point, you need to apply what you've learned to analyze the figure and other data to solve the problem.Because this problem may be difficult to envision, a diagram is extremely helpful. Note that although the hiker makes a significant (100 meter) change in elevation over this walk, the difference between the actual distance he walks and the horizontal distance is small--only about 12 meters.

Use this step to fill in as much missing information in your diagram as you can.At this point, you need to apply what you've learned to analyze the figure and other data to solve the problem.Because this problem may be difficult to envision, a diagram is extremely helpful. Note that although the hiker makes a significant (100 meter) change in elevation over this walk, the difference between the actual distance he walks and the horizontal distance is small--only about 12 meters.

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This approach is similar to that for solving almost a word problem, but is geared slightly more toward the characteristics of geometry problems in particular.

In some cases, you may need a length; in others, an area or angle measure.

You may, for example, need to apply the Pythagorean theorem, or you may need to calculate the perimeter of a figure.

Whatever the details of the problem, you will need to apply your skills in geometry in an appropriate manner.

Keep careful track of the units you are using throughout the problem.

If no units are given, simply use the generic term "units" in place of inches or meters, for example. Perhaps you can show two triangles to be congruent or similar, or perhaps you can identify congruent segments or angles.

Even if you only use a rough sketch, however, making a visual representation of the problem can help you organize your thoughts and keep track of important information such as the relationship of line segments and angles as well as the measures thereof.

If you are calculating an area, for instance, you may need to take measurements of certain lengths (alternatively, these may be provided to you).

We are told in the problem that the inside border of each garden meets the fence at the same angle in every case; thus, we can conclude (as shown below) that the triangles are all isosceles (and that the triangles with the same side lengths are congruent by the ASA condition).

Often, you will be asked to solve problems involving geometric relationships or other shapes.

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