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6.3 Use Similar Polygons

6.3 Use Similar Polygons. Hubarth Geometry. In geometry, two figures that have the same shape are called similar. Two polygons are similar polygons if corresponding angles are congruent and Corresponding side lengths are proportional. C. G. B. F. E. H. D. A.

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6.3 Use Similar Polygons

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  1. 6.3 Use Similar Polygons Hubarth Geometry

  2. In geometry, two figures that have the same shape are called similar. Two polygons are similar polygons if corresponding angles are congruent and Corresponding side lengths are proportional. C G B F E H D A

  3. In the diagram, ∆RST ~ ∆XYZ a. List all pairs of congruent a. angles. 5 ST 30 25 TR 5 RS 5 20 b. b. Check that the ratios of ; ; = = = = = = 3 15 3 ZX 3 18 XY 12 YZ corresponding side lengths are equal. ~ ~ ~ R X, T Z and Y S = = = c. Write the ratios of the corresponding side lengths in a statement of proportionality. . TR ST RS = = YZ ZX XY Ex 1 Use Similarity Statements c. Because the ratios in part (b) are equal,

  4. Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXWto FGHJ. 5 5 5 5 5 = = = = 30 15 20 25 XW ZY WZ YX 4 4 4 4 4 HJ JF 16 GH 20 FG 12 24 So ZYXW ~ FGHJ. The scale factor of ZYXWto FGHJis . = = = = Ex 2 Find the Scale factor

  5. In the diagram, ∆DEF ~ ∆MNP.Find the value of x. = NP MN DE EF 20 12 = x 9 Ex 3 Use Similar Polygons The triangles are similar, so the corresponding side lengths are proportional. Write proportion. Substitute. 12x = 180 Cross Products Property x = 15 Solve for x.

  6. Perimeters of Similar Polygons D A C B F E

  7. A town is building a new swimming pool. An Olympic pool is rectangular with length 50 meters and width 25 meters. The new pool will be similar in shape, but only 40 meters long. b. b. Find the perimeter of an Olympic pool and the new pool. The perimeter of an Olympic pool is 2(50) + 2(25)=150 meters. You can use Theorem 6.1 to find the perimeter xof the new pool. x = a. Because the new pool will be similar to an Olympic pool, the scale factor is the ratio of the lengths, 150 4 4 40 5 5 50 = a. Find the scale factor of the new pool to an Olympic pool. Ex 4 Find Perimeters of Similar Figures Use Theorem 6.1 to write a proportion. x = 120 Multiply each side by 150 and simplify.

  8. In the diagram, ∆TPR~ ∆XPZ. Find the length of the altitude PS. = PS TR 3 3 12 3 4 4 XZ 4 PY 16 PS = 20 = PS 15 6 + 6 = = = 8 + 8 Key concepts Corresponding Lengths in Similar Polygons If two polygons are similar, then the ration of any two corresponding lengths in the polygons is Equal to the scale factor of the similar polygons. Ex 5 Use a Scale Factor First, find the scale factor of ∆TPRto ∆XPZ. Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion. Write proportion. Substitute 20 for PY. Multiply each side by 20 and simplify.

  9. Practice Determine whether the polygons are similar. If they are similar, write a similarity statement and find the scale factor of Fig. B to Fig. A. Y E N P 1. A 2. A B S T 8 6 12 9 B 12 Z X 10 12 F D 18 R V 6 U Q 9 P S x 14 7 8 T U 9 Q 18 R

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