Find AB if AD = 3 and DC = 9.

Question

In the figure, ∠ABC ≅ ∠ADB.

Find AB if AD = 3 and DC = 9.

Answer 1

The triangles are similar not congruent. Because corresponding parts of similar triangles are in proportion:

AC = AB

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AB AD

Because AC = AD + DC = 3 + 9 = 12 and AD = 3:

12 = AB

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AB 3

AB^2 = 36

AB = 6