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Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Understand the different theorems to prove similar triangles using formulas and derivations.
Properties of Similar Triangles Formulas. Has the same shape but size may vary; in ΔZYX and ΔPQR, ΔZYX > ΔPQR in size. Has each pair of corresponding angles congruent; here ∠Z ≅ ∠P, ∠Y ≅∠Q, and ∠X ≅ ∠R. Has the ratio of the corresponding sides same: here x/r = z/p = y/q.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around). These triangles are all similar: (Equal angles have been marked with the same number of arcs)
Similar Triangles. Two triangles are similar if they have the same shape but not necessarily the same size. The corresponding angles are equal, and the corresponding sides are proportional. We can think of one similar triangle as an enlargement or a reduction of the other. (See the figures below.)
Properties of Similar Triangles. Here are the three most commonly used properties of similar triangles. We’ll use the triangles below as examples. Property 1. Corresponding angles are equal.
Properties of Similar Triangles. Corresponding angles are congruent (same measure) So in the figure above, the angle P=P', Q=Q', and R=R'. Corresponding sides are all in the same proportion. Above, PQ is twice the length of P'Q'. Therefore, the other pairs of sides are also in that proportion. PR is twice P'R' and RQ is twice R'Q'.