Similar Figures – Outschool
Similar Figures Lesson
Similar figures have the same shape, but are not necessarily the same size. This means
1) corresponding angles have the same measure
and
2) ratios between corresponding side lengths are equal.
For example, if two triangles are similar and one side is twice as long as the corresponding side in the first triangle…
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then all the sides are twice as long in the 2nd triangle.
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Ratios between corresponding side lengths are equal:
[latex]frac{20}{10} = frac{18}{9} = frac{12}{6}[/latex] → [latex]2[/latex]
The scale factor of the second triangle to the first triangle is 2 to 1.
Likewise, if two quadrilaterals are similar, and one side is 1.5 times the length of the corresponding side in the first figure,
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then every side in the 2nd quadrilateral is 1.5 times the length of the corresponding sides in the 1st quadrilateral.
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Please note, that again, the ratios between corresponding side lengths are equal:
[latex]frac{21}{14} = frac{12}{8}[/latex] → [latex]1.5[/latex]
Key 1: The ratios of corresponding side lengths in similar figures are always equal.
Key 2: Because ratios of corresponding sides are always equal in similar figures, we can set up proportions to find missing side lengths and perimeters.
Example
In the figure below, ΔABC and ΔDEF are similar triangles with the given side lengths in centimeters. To the nearest tenth of a centimeter, what is the perimeter of ΔABC?
Step 1: Find the perimeter of ΔDEF.
Perimeter = 3 + 4 + 4.5
Perimeter = 11.5
Step 2: Set up a proportion with corresponding perimeters!
Use the corresponding sides with given lengths to set up the proportion:
[latex]frac{3}{7} = frac{11.5}{p}[/latex] (Cross multiply.)
3p = 80.5 (Divide both sides by 3.)
p ≈ 26.8
The perimeter of ΔABC is approximately 26.8 centimeters.