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Warm up (ti)

Warm up (ti). Find the measures of the angles in the figure below. <U <W Solve the proportion. If your answers are fractions, leave in simplest, improper fractional form. 2/x = 5/20 18/5 = 12/t. U. V. 61. 58. W. X. Warm up (TI). Decide whether the statement is true or false. (Q 1&2)

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Warm up (ti)

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  1. Warm up (ti) • Find the measures of the angles in the figure below. • <U • <W • Solve the proportion. If your answers are fractions, leave in simplest, improper fractional form. • 2/x = 5/20 • 18/5 = 12/t U V 61 58 W X

  2. Warm up (TI) • Decide whether the statement is true or false. (Q 1&2) • If a/b = (b-1)/8, then (a+6)/6 = (b+8)/8. • If x/y = x+5/y+3, then x/x+5 = y/y+3. • Find the geometric mean of 9 and 25. • Given PT/PR = QU/QS, find SU. P Q 8 10 R S 10 U T

  3. Similar Polygons Chapter 8 Section 3

  4. Similar Polygons • If two polygons are similar, then they have the same shape but not necessarily the same size… • Since they have the same shape…their angles will be exactly the same. • Since they are different sizes…the corresponding sides will form equal ratios (aka…they’re proportional!) 10cm 120 60 5cm 12cm 12cm 120 60 6cm 6cm 120 60 60 120 5cm 10cm

  5. Similarity • Symbol for similarity: ~ Similarity statement: PENTA~HIJKL N J E T I K A L P H

  6. Similarity statement: PENTA~HIJKL • This statement means: m<P = m<H m<E = m<I m<N = m<J m<T = m<K m<A = m<L • And (statement of proportionality) PE/HI=EN/IJ=NT/JK=TA/KL=PA/HL N J E T I K A L P H

  7. Are these figures similar? 10 8 15 3

  8. What about these? 6 12 89 89 5 4 10 102 82 8 87 7 82 14 If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. What is the scale factor of the small figure to the large figure?

  9. Theorem • If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. (ratio of the perimeters = the scale factor)

  10. Example • Given TUVW ~ ABCD • List all pairs of congruent angles and write the statement of proportionality. • What is the scale factor? • Find the length of TW. • Find the measure of <TUV. 15 U T 9 A B 6 70° W V D C 23

  11. Example • Parallelogram ABCD is similar to parallelogram GBEF. Find the value of y. E B C 12 G y F 15 A D 24

  12. Example • ∆UVW ~ ∆YXW. Find the value of a. U V a 5 W 6.4 12 X Y

  13. Complete Assignment #3

  14. 8.4 Similar Triangles • Shortcuts for proving triangles similar: AA Similarity If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. ∆JKL ~ ∆XYZby AA similarity K Y L Z J X

  15. Example • Explain why ∆WVX ~ ∆WZY. W X V Y Z

  16. 33 M L N 20 Q P Example • In the diagram, is ∆LMN ~ ∆PQN? Explain. • Find m<M and m<P. • Find MN and QM. 106° 36° 30

  17. If two polygons are similar, then the ratio of any two corresponding lengths (like the medians, altitudes, etc..) will be equal to the scale factor. E Find the length of EH. *Hint…separate the triangles. C 6 D A B F H 7.5 5

  18. Complete assignment #4

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