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How to Find Measures of Similar Triangles

Triangles are three-sided polygons. Similar triangles have equal corresponding angles. The corresponding sides are proportional but have different lengths. You can find the missing sides by forming proportions using the known side lengths. A proportion is at least two fractions that are equivalent. Corresponding indicates the angles that are the same and have a similar location from one triangle to the other. Corresponding sides are located on different triangles but have the same location and proportional relationship with adjacent sides.

Instructions

    • 1

      Designate and label the corresponding angles. For example, you may label the angles of triangle 1 as Angle 1: 30 degrees, Angle 2: 60 degrees and Angle 3: 90 degrees. Do the same with triangle 2, noticing that the angle that appears to be the smallest is 30 degrees also. The angle that appears to be the largest is 90 degrees. The other medium sized angle is 60 degrees.

    • 2

      Label the corresponding sides on the triangle. For example, for triangle 1, write side 1-1, 1-2 and 1-3. For triangle 2, write sides 2-1, 2-2 and 2-3, labeling according to the location of the sides relevant to corresponding sides of the other triangle.

    • 3

      Form a proportion with three known and one unknown side lengths.

      Example 1: side 1-1/side 1-2 = side 2-1/side 2-2. Similarly,

      Example 2: side 1-1/side 2-1 = side1-2/side 2-2

    • 4

      Substitute the known and unknown information. Write an "n" for the unknown quantity.

      Example 1: 3/4 = 6/x, where side 2-2 is unknown.

      Example 2: 3/6 = 4/x, where side 2-2 is unknown.

    • 5

      Multiply the side corresponding to the missing length by the scale factor to determine the missing side length.

      For example 1: 3 * scale factor = 6. The scale factor is 2 because 3 * 2 = 6.

      Thus, multiply the missing length's corresponding side by 2 (the scale factor) to get 8.

      Side 4 * 2 = 8; 8 is the missing length.

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