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Triangle with parallel line segment dividing sides proportionally.

Triangle ADE with line segment BC parallel to DE, where AB = 6 cm, AC = 9 cm, BC = 8 cm, and DE = x cm.

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Show Answer Key & Explanations Step-by-step solution for: Find missing lengths in similar shapes which have sides ...

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Looking at this zoomed-in view of side AE, I can clearly see that AC is labeled as 6 cm and the entire length AE is labeled as 9 cm. This confirms my earlier observation that CE = AE - AC = 9 cm - 6 cm = 3 cm.

Since BC is parallel to DE, triangles ABC and ADE are similar by the AA (Angle-Angle) similarity criterion. This means their corresponding sides are proportional.

The proportion based on similar triangles is:
AC/AE = BC/DE

Substituting the known values:
6/9 = 8/x

Now I'll solve for x:
6x = 9 × 8
6x = 72
x = 72/6
x = 12

Therefore, the length of DE is 12 cm.

The solution is: x = 12 cm

Parent Tip: Review the logic above to help your child master the concept of finding missing sides of similar figures worksheet.

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