Find the area of Δ STU.įigure 4 Using the scale factor to determine the relationship between the areas of similar triangles. Theorem 61: If two similar triangles have a scale factor of a : b, then the ratio of their areas is a 2 : b 2.Įxample 2: In Figure 4, Δ PQR∼ Δ STU.
Now you can compare the ratio of the areas of these similar triangles. You can now find the area of each triangle.įigure 3 Finding the areas of similar right triangles whose scale factor is 2 : 3. Because GH ⊥ GI and JK ⊥ JL , they can be considered base and height for each triangle. Find the perimeter of Δ DEFįigure 3 shows two similar right triangles whose scale factor is 2 : 3. Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.Įxample 1: In Figure 2, Δ ABC∼ Δ DEF. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. The perimeter of Δ ABC is 24 inches, and the perimeter of Δ DEF is 12 inches. It is then said that the scale factor of these two similar triangles is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5. In Figure 1, Δ ABC∼ Δ DEF.įigure 1 Similar triangles whose scale factor is 2 : 1. When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.
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