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# In the figure below, triangle ABC is similar to triangle PQR, as shown below: What is the length of side PQ? A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.

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For two polygons to be considered similar, corresponding angles must be congruent and, at the same time, the sides of corresponding sides must be proportional. The side corresponding to QR is BC, BC = 2 and QR = 12 As you can see, QR is 6 times more than in BC, and so PQ must be proportional to AB by the same factor. if AB is 4 then multiply that by 6:4 x 6 = 24Line PQ is 24