ACT Preparation / Unit 13 ACT 1220 worked example, 60 to 90 seconds
Solving Similar Triangles for a Side
The idea
A missing side in similar triangles is found in three steps. First, confirm similarity, usually by AA, and match the vertices: equal angles correspond. Second, write a proportion with corresponding sides in the same order, small over large on both sides. Third, cross-multiply and solve.
In practice
Worked example: in triangle ABC, a segment DE is drawn parallel to BC, with D on AB and E on AC. AD = 4, AB = 12 and DE = 6. Triangles ADE and ABC share angle A, and the parallel line makes their other angles equal, so they are similar by AA. Proportion: 4/12 = 6/BC, so BC = 18.
Where people slip
Use whole sides, not pieces: AB is 12, the full side, while DB, the leftover piece of 8, corresponds to nothing in the small triangle.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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