All subjects basic Ideas Parallel currently triangles polygons Perimeter and Area Similarity appropriate Angles circles Geometric Solids coordinate Geometry

When 2 triangles are similar, the decreased ratio of any type of two corresponding sides is called thescale factorof the comparable triangles. In number 1, ΔABC∼ ΔDEF.

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Figure 1 comparable triangles who scale element is 2 : 1.

The ratios of corresponding sides space 6/3, 8/4, 10/5. This all reduce to 2/1. That is then stated that the scale factor of this two similar triangles is 2 : 1.

The perimeter of ΔABCis 24 inches, and also the perimeter the ΔDEFis 12 inches. Once you compare the ratios that the perimeters of these comparable triangles, you likewise get 2 : 1. This leader to the adhering to theorem.

Theorem 60:If two comparable triangles have a scale factor ofa:b,then the proportion of their perimeters isa:b.

Example 1:In number 2, ΔABC∼ ΔDEF. Find the perimeter that ΔDEF

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Figure 2Perimeter of similar triangles.

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Figure 3shows two comparable right triangles who scale element is 2 : 3. BecauseGHGIandJKJL, they deserve to be considered base and also height because that each triangle. You deserve to now find the area of every triangle.

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Figure 3 recognize the locations of comparable right triangles who scale variable is 2 : 3.

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Now you deserve to compare the proportion of the areas of these comparable triangles.

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This leader to the following theorem:

Theorem 61:If two similar triangles have a scale element ofa:b, then the ratio of their locations isa2:b2.

Example 2:In number 4, ΔPQR∼ ΔSTU. Uncover the area that ΔSTU.

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Figure 4 Using the scale aspect to recognize the relationship in between the areas of comparable triangles.

The scale variable of these comparable triangles is 5 : 8.

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Example 3:The perimeters the two similar triangles is in the ratio 3 : 4. The amount of their locations is 75 cm2. Find the area of every triangle.

If you speak to the triangles Δ1and Δ2, then

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According toTheorem 60,this also way that the scale variable of this two comparable triangles is 3 : 4.

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Because the sum of the locations is 75 cm2, you get

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Example 4:The areas of two similar triangles are 45 cm2and 80 cm2. The amount of their perimeters is 35 cm. Discover the perimeter of every triangle.

Call the two triangles Δ1and Δ2and permit the scale factor of the two comparable triangles bea:b.

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a:bis the reduced type of the range factor. 3 : 4 is then the reduced kind of the compare of the perimeters.