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Geometry

Geometry. Lesson 7 – 2 Similar Polygons. Objective: Use proportions to identify similar polygons. Solve problems using the properties of similar polygons. Similar Polygons. What does it mean to be similar?. Same shape, but not necessarily the same size. Similar polygons.

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Geometry

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  1. Geometry Lesson 7 – 2 Similar Polygons Objective: Use proportions to identify similar polygons. Solve problems using the properties of similar polygons.

  2. Similar Polygons • What does it mean to be similar? Same shape, but not necessarily the same size.

  3. Similar polygons • Two polygons are similar if and only if their corresponding angles are congruent and corresponding side lengths are proportional. ABCD is similar to WXYZ Means similar to

  4. If FGH ~ JKL, list all pairs of congruent angles and write a proportion that relates the corresponding sides.

  5. Scale Factor • The ratio of the lengths of the corresponding sides of two similar polygons 6/3 = 2 = 1/2 3/6

  6. Kuma wants to use the rectangular photo shown as the background for her computer’s desktop, but she needs to resize it. Determine whether the following rectangular images are similar. If so, write the similarity statement and scale factor. Explain your reasoning. Corresponding angles are congruent since all are rectangles. Not proportional Cont..

  7. Since the angles are congruent and the sides are proportional, ABCD ~ JKLM with a scale factor of 2/3

  8. Determine if the triangles are similar. If so write the similarity statement and scale factor. Angles are congruent since 2 angles are congruent so are the 3rd angles. Check that all of the proportions are true. Yes the triangles are proportional. 1.25 = 1.25 NQP ~ RST 1.25 = 1.25 Scale factor: 1.25 = 1.25

  9. ACDF ~ VWYZ Make sure the right Things are paired up. Use your statement! • Find x. • Find y. 6x = 90 x = 15 27y – 9 = 72 27y = 81 y = 3

  10. Triangle JLM ~ Triangle QST • Find x • Find y 12x – 6 = 12 12x = 18 x = 1.5 6y – 4 = 20 6y = 24 y = 4

  11. Theorem • Perimeter of similar polygon • If two polygons are similar, then their perimeters are proportional to the scale factor be

  12. 8 Tells what the order should be for scale factor. • If ABCDE ~ PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon. Scale factor: 4 Scale factor: 4/3 Perimeter PQRST 22.5 Perimeter ABCDE 30 4x = 90 x = 22.5

  13. If MNPQ ~ XYZW, find the scale factor of MNPQ to XYZW and the perimeter of each polygon. Scale factor: 2x = 34 Scale factor: 2 Perimeter WXYZ = 17 Perimeter MNPQ = 34 x = 17

  14. Homework • Pg. 468 1 – 7 all, 8 – 26 E, 40 – 44 E, 52, 56 – 72 E

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