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Given triangle ABC and a point D on the side AC. Suppose AB=6, BC=8, AC=9, and AD=4. Find BD
Triangle ABD and ACB are similar with angle A = angle A, angle ABD = ACB. Similar by AA. AB:AC = 6:9, AD:AB = 4:6. This means that the ratio of triangle ABD : ACB is 1 : 1.5. Because of this, since BD corresponds to BC, then BD : 8 = 1 : 1.5, and BD = 8 divided by 1.5, so BD = 5 1/3
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