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Warm Up

Warm Up. At a certain time of day, a 6 ft man casts a 4 ft shadow. At the same time of day, how long is the shadow of a tree that is 27 feet tall ? 3) ΔABC~ΔDEF. Solve for y . G. E. 2) Find JG . J. 6. x. H. 12. 4. F. D. A. 35 . 10 . Y. 14. 30°. 30°. C. B. F. E.

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Warm Up

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  1. Warm Up • At a certain time of day, a 6 ft man casts a 4 ft shadow. At the same time of day, how long is the shadow of a tree that is 27 feet tall? 3) ΔABC~ΔDEF. Solve for y. G E 2) Find JG J 6 x H 12 4 F D A 35 10 Y 14 30° 30° C B F E

  2. HW Answers P 385 #2-16 even • No; not enough info given 4) Yes, AA ~ Post. Triangle FHG ~ KHJ 6) No 8) Yes, SAS ~ Thm. Triangle NMP ~ NQR • AA~ Post; 7.5 • AA~ Post; 12 5/6 14) AA ~ Post; 8 • SAS ~ Thm. 12m 18) AA~ Post; 15 ft 9in

  3. Due at the end of class. Practice 7-3 in Workbook p383 #1-12 all • Do problems in your notebook, Write the question for full credit!! Show all work. Quiz Tomorrow on Proving Triangles Similar.

  4. Check Answers to Yesterday’s Assignment • Workbook

  5. Similarity in Right Triangles Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Knowing this theorem, how can you solve for x and y. x y 4 5

  6. Geometric Mean • Proportions in which the means are equal. • For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that: a/x = x/b, then x = _____ • Ex. Find the geometric mean of 4 and 18.

  7. Corollary to previous theorem Corollary 1: The length of the altitude of the hypotenuse of a right triangle is the geom. Mean of the lengths of the segments of the hypotenuse. Corollary 2: The altitude of the hyp. Of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geom. mean of the length of the adjacent hyp. segment and the length of the hyp.

  8. Solve for x and y. C y 6 A B D x 2

  9. Quiz/Assignment • Complete Quiz, when you are finished, give Ms. Malik your quiz and begin your homework assignment. • Due Wednesday • P 394 #2-20 even, 34-36 • P 401 #1-23 odd (SHOW WORK!!) • Set up all proportions and show work for FULL credit.

  10. Warm Up C x y A B D 12 4

  11. HW Questions?

  12. Workbook Practice 7-4 • Whiteboards # 1- 3 # 13 - 18

  13. Triangle Proportionality Theorem • If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Q R S X Y

  14. Example B 4 • Find the value of x or y. 2. G 1. 12 C 5 H A x

  15. Find the value of x or y S L M • You try on white boards. y 4 2 3. P 4. Q U x 14 5 R N 10 V 4 T

  16. 2 Transversals Proportionality Corollary • If three parallel lines intersect two transversals, then the segments intersected on the transversals are proportional. c a d b

  17. Practice: 1. Find x and y A 4 B 9 10 6 D 7.2 2. Find the length of LN to the nearest tenth. C N M L 12 K

  18. On Whiteboards.. 3. Find the length of LM and MN. A 4. Find x 10 B 2 C 6 D N M L 25 K

  19. Triangle Angle-Bisector Theorem • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. A B C D

  20. Find the value of x. Practice 2. Find VT R 24 1. 10 V S T 4

  21. Your turn on wb… 4. Find DC 3. Find x A 5 14 8 B C 12 D

  22. Groups

  23. Exit Pass G E 1.Find JG J x 6 H 11 4 F

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