To find the ratio of corresponding sides between two similar figures, identify matching sides, then express and simplify the ratio between their lengths.
Here's a breakdown of the process:
-
Identify Corresponding Sides: This is the crucial first step. Corresponding sides are the sides that occupy the same relative position in two similar figures. Look for clues like angle markings, descriptions in the problem, or visual similarity.
-
Measure or Determine the Length of the Sides: You'll need to know the lengths of the corresponding sides you identified. This might be given directly in the problem or require some calculation using other geometric principles (like the Pythagorean theorem).
-
Write the Ratio: Once you have the lengths, write the ratio of the length of a side in the first figure to the length of its corresponding side in the second figure. The order matters! For example, if side 'a' in figure A corresponds to side 'b' in figure B, the ratio would be a/b (or a:b).
-
Simplify the Ratio: Express the ratio in its simplest form. This often involves dividing both parts of the ratio by their greatest common factor.
Example:
Let's say you have two similar triangles.
- Triangle 1 has a side length of 6.
- Triangle 2 has a corresponding side length of 9.
- Corresponding Sides: We're told these sides correspond.
- Side Lengths: Side lengths are 6 and 9.
- Write the Ratio: The ratio is 6/9.
- Simplify the Ratio: 6/9 simplifies to 2/3. Therefore, the ratio of the corresponding sides is 2:3.
Important Considerations:
- Similarity is Key: This method only works for similar figures. Similar figures have the same shape but can be different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.
- Consistency: When comparing multiple pairs of corresponding sides, the ratio should be the same for all pairs if the figures are truly similar.
- Units: Make sure the measurements are in the same units before writing the ratio. If one side is measured in inches and the corresponding side is measured in feet, convert them to the same unit (e.g., convert feet to inches) before calculating the ratio.
- Area and Side Length Ratios: Remember, the ratio of the areas of two similar figures is the square of the ratio of their corresponding sides. If the side length ratio is 2/3, the area ratio is (2/3)^2 = 4/9.
