# If DB = 24, AE = 3, and EC= 18, what is AD?

According to the Triangle Proportionality Theorem parallel lines cut triangles into proportional parts.

So we can assume:

From there we can just solve:

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To find AD, we can use the property of similar triangles. Triangles ADE and ABC are similar since they share angle A and have parallel sides (DE and BC) due to transversals AE and DC.

Using the property of similar triangles:

AD/AB = AE/AC

Substituting the given values:

AD/ (AD + DB) = AE/(AE + EC)

Solving for AD:

AD/(AD + 24) = 3/(3 + 18)

AD/(AD + 24) = 3/21

Cross multiply:

21AD = 3(AD + 24)

21AD = 3AD + 72

18AD = 72

AD = 72/18

AD = 4

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