Similar Polygons Date: Per:
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1 Math 2 Unit 6 Worksheet 1 Name: Similar Polygons Date: Per: [1-2] List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons. 1. AA BB CC DD AAAA WWWW = BBBB XXXX = = 2. GG HH II GGGG KKKK = = [3-6] Determine whether the polygons are similar. a) Give the scale factor of the left polygon to the right polygon. b) Complete the statement of similarity. If not similar, write not similar for both a and b and explain a) SF = a) SF = b) CCCCCCCC~ b) QQQQQQ~ a) SF = a) SF = b) LLLLLLLL~ b) BBBBBB~ 7. In the diagram below, NNNNNN~ WWWWWW. Find each of the following: a) the scale factor of NNNNNN to WWWWWW = b) mm XX = c) mm YY = d) WWWW = e) NNNN = Math 2 Unit 6 Worksheet 1
2 8. In the diagram below, PPPPPP~ DDDDDD. Find each of the following: a) the scale factor of PPPPPP to DDDDDD = b) mm DD = c) mm RR = d) mm PP = e) DDDD = f) FFFF = 9. The quadrilaterals shown are similar. Find the scale factor of the larger quadrilateral to the smaller, then find the values of xx, yy, and zz. yy a) the scale factor 8 35 b) xx = xx zz 6 c) yy = 14 4 d) zz = 10. Find the value of zz. Give the scale factor of the polygons. JJJJJJ~ QQQQQQ a) zz = b) the scale factor of JJJJJJ to QQQQQQ = [11-20] Given the similar polygons, use a proportion to find the value of each variable. 11. JJJJJJ~ NNNNNN 12. DDDDDD~ HHHHHH a) xx = a) xx = b) yy = b) yy = Math 2 Unit 6 Worksheet 1
3 13. QQQQQQ~ TTTTTT 14. AAAAAA~ AAAAAA a) xx = a) xx = 15. MMMMMM~ QQQQQQ 16. BBBBBB~ FFFFFF a) xx = a) xx = 17. KKKKKKKK~ PPPPPPPP 18. RRRRRR~ YYYYYY a) xx = a) xx = 19. CCCCCC~ FFFFFF a) xx = 20. If KKKKKK~ PPPPPP with a scale factor of 3: 5, find the perimeter of PPPPPP a) perimeter PPPPPP = Math 2 Unit 6 Worksheet 1
4 Math 2 Unit 6 Worksheet 2 Name: Proving Triangles Similar Date: Per: [1-6] Determine if the triangles are similar. a) Complete the statement of similarity. b) State the postulate or theorem that justifies the similarity. If not similar, write not similar for both a and b and explain. BB RR EE XX AA DD CC ZZ a) AAAAAA~ a) PPPPPP~ b) b) AA MM 6 8 FF 5 CC 4 BB 10 PP 8 RR SS 4 TT 9 a) AAAAAA~ a) IIIIII~ NN 6 b) b) 5. SS QQ PP 6. RR XX RR a) PPPPPP~ a) PPPPPP~ ZZ b) b) Math 2 Unit 6 Worksheet 2
5 7. A 6 ft tall man is standing next to a tree. The man s shadow is 4 ft long. At the same time, the shadow of the tree is 10 ft long. How tall is the tree? 8. A 1.4 m tall child is standing next to a flagpole. The child s shadow is 1.2 m long. At the same time, the shadow of the flagpole is 7.5 m long. How tall is the flagpole? 9. Victoria wants to find the height of a flagpole. Victoria is 5 ft tall, the flagpole s shadow is 70 ft long, and her shadow is 12 ft long. Find the height of the flagpole. 10. REVIEW: The quadrilaterals shown are similar. Find the scale factor of the larger quadrilateral to the smaller, then find the values of aa, bb, and cc. a) the scale factor 15 b) aa = c) bb = 35 aa cc bb 6 d) cc = 12 8 [11-14] Explain why the triangles are similar. Then find the value of xx xx + 4 xx 7 10 xx = xx = Math 2 Unit 6 Worksheet 2
6 xx = xx = 15. The below figure contains 3 similar triangles. BB yy xx AA 56ᵒ 2 DD 8 34ᵒ CC a) Label these three triangles with correct vertices, side lengths, and angle measures using the information in the original figure. b) Using 2 to 4 complete sentences explain in detail how you know the largest and middle-sized triangles must be similar. [c-d] Round answer to nearest tenth. c) xx = d) yy = Math 2 Unit 6 Worksheet 2
7 Math 2 Unit 6 Worksheet 3 Name: Proportions in Triangles Date: Per: [1-10] Find the missing length. 1.? = 2.? = 10 3.? = 4. xx = 5.? = 6.? = 7.? = 8.? = 21? Math 2 Unit 6 Worksheet 3
8 9.? = 10. xx = [11-14] Solve for xx. 11. xx = 12. xx = 13. xx = 14. xx = Math 2 Unit 6 Worksheet 3
9 Math 2 Unit 6 Worksheet 4 Name: Dilations Date: Per: [1-5] The dashed-line figure is a dilation image of the solid-line figure. The labeled point is the center of dilation. Tell whether the dilation is: a) an enlargement or a reduction and b) find the scale factor of the dilation. 1. a) b) scale factor 2. a) b) scale factor 3. a) b) scale factor 4. a) b) scale factor 5. a) b) scale factor Math 2 Unit 6 Worksheet 4
10 Dilation - When the Center of Dilation is Not the Origin 6. Dilate ΔΔΔΔΔΔΔΔ by a factor of 4, using PP ( 12, 10) as the center of dilation. 7. Dilate ΔΔΔΔΔΔΔΔ by a factor of 1, 2 using JJ (10, 4) as the center of dilation. GG(8, 10) HH(10, 12) II(8, 14) AA( 10, 8) BB( 10, 5) CC( 7, 8) 8. Dilate ΔΔΔΔΔΔΔΔ by a factor of 2, using QQ (12, 3) as the center of dilation. XX(7, 9) YY(8, 3) ZZ(13, 7) Math 2 Unit 6 Worksheet 4
11 9. Dilate rectangle AAAAAAAA by a factor of 3, using PP ( 13, 3) as the center of dilation. AA( 11, 3) BB( 11, 6) CC( 6, 6) DD( 6, 3) 10. Find the perimeter and area of each rectangle from problem 9. AAAAAAAA PP =, AA = AA BB CC DD PP =, AA = What is the scale factor of AAAAAAAA to AA BB CC DD? What is the ratio of the perimeters? What is the ratio of the areas? If the ratio of two similar figures is a to b, then The ratio of any length is The ratio of the perimeter is The ratio of the area is Math 2 Unit 6 Worksheet 4
12 11. DDDDDD is a dilation of AAAAAA with a center of point PP. D F A C P B E a) Is the dilation an enlargement or reduction? b) What is the scale factor? c) Perimeter of AAAAAA Area of AAAAAA Perimeter of DDDDDD Area of DDDDDD d) What is the relationship between the perimeters of similar figures? e) What is the relationship between the areas of similar figures? Math 2 Unit 6 Worksheet 4
13 Math 2 Unit 6 Worksheet 5 Name: Dilations Centered at (0,0) Date: Per: [1-4] Determine if the dilation is a reduction or enlargement of the figure using (0,0) as the center of dilation. Graph the image of the figure using the dilation given. 1. Dilation of 2: 2. Dilation of 0.5: 3. Dilation of 3 2 : 4. Dilation of 1 2 : [5-7] Write a rule to describe each dilation. Example Rule: ( xx, yy ) ( 2xx, 2yy) 5. Rule: (, ) (, ) Math 2 Unit 6 Worksheet 5
14 6. Rule: (, ) (, ) 7. Rule: (, ) (, ) [8-12] Determine if the scale factor will reduce or enlarge the figure. Find the coordinates of the vertices of each figure after the given dilation. 8. Dilation of 2: WW ( 2, 1); EE ( 2, 1); JJ (2, 1); XX (2, 0) WW (, ); EE (, ); JJ (, ); XX (, ) 9. Dilation of 3 2 : EE ( 2, 0); KK (1, 2); YY (3, 2) EE (, ); KK (, ); YY (, ) 10. Dilation of 5 2 : FF ( 1, 1); ZZ (2, 2); EE (0, 1) FF (, ); ZZ (, ); EE (, ) 11. Dilation of 1 2 : NN ( 1, 3); CC (0, 2); II (3, 5) NN (, ); CC (, ); II (, ) [12-14] Write a rule to describe each dilation. Example: GG (2, 4); AA (1, 1); LL (2, 1); TT (3, 4) GG (0.5, 1); AA (0.25, 0.25); LL (0.5, 0.25); TT (0.75, 1) Rule: ( xx, yy ) ( 1 4 xx, 1 4 yy) 12. SS ( 4, 1); AA ( 3, 4); XX (0, 1) SS ( 12, 3); AA ( 9, 12); XX (0, 3) Rule: ( xx, yy ) (, ) 13. HH ( 2, 0); YY ( 1, 4); BB (3, 1) HH ( 0.5, 0); YY ( 0.25, 1); BB (0.75, 0.25) Rule: ( xx, yy ) (, ) 14. UU ( 4, 5); YY ( 5, 1); PP ( 4, 1); KK ( 3, 3) UU ( 2, 2.5); YY ( 2.5, 0.5); PP ( 2, 0.5); KK ( 1.5, 1.5) Rule: ( xx, yy ) (, ) Math 2 Unit 6 Worksheet 5
15 Math 2 Unit 6 Name: Review Worksheet Date: Per: [1-9] Select the correct multiple choice response. Show all work Solve the proportion: = xx 2. Solve the proportion: a. 24 a. 9 3 = xx b. 21 b. 17 c. 25 c. 25 d. 20 d Given: KKKKKK~ KKKKKK Which side below makes the proportion KKKK a. KKKK KKKK =? KKKK true? L K M b. KKKK c. LLLL Q P d. QQQQ 4. Which proportion is accurate for the diagram shown? dd a. h = cc kk b. dd = kk h cc c. dd h = cc cc+kk d. dd h = cc cc kk 5. A 6-foot boy has a shadow that is 4 feet. At the same time of day a tree has a shadow that is 24 feet. What is the height of the tree? a. 12 ft. b. 18 ft. c. 24 ft. d. 36 ft. 6. Which similarity statement below is true for the two triangles? a. BCA XZY B b. ABC ZXY c. BAC ZXY 30 d. ABC YZX A 25 X C 7. AA BB CC is the image of AAAAAA under a dilation with a scale factor of 2.5 centered at the origin. If AAAA = 8 units, what is the unit length of AA BB? a. 20 b. 16 c. 4 d. 2.5 Y Z Math 2 Unit 6 Review Worksheet
16 8. Using the diagram below, AAAAAA~ GGGGGG 9. Using the diagram below, AAAAAAAAAA WWWWWWWWWW a) mm BB = a) mm AA = b) mm LL = b) mm PP = c) Find the scale factor of the smaller triangle to the larger G F A 25 R A E Z 85 W B 14 C C J L B X P [10-14] Determine if the triangles are similar. a) Complete the statement of similarity. b) State the postulate or theorem that justifies the similarity. If not similar, write not similar for both a and b and explain. 10. a) TTTTTT~ 11. a) UUUUUU~ 12. a) RRRRRR~ b) b) b) C P R 6 T 9 L Z H 13. a) LLLLLL~ 14. a) KKKKKK~ b) b) A E 8888 U D G 15 9 K N 6 8 H L [15-18] The following figures are similar. Find the values of the variable(s). 15. xx = yy = 16. xx = yy = y x 9 y 18 x Math 2 Unit 6 Review Worksheet
17 17. xx = 18. xx = x 19. xx = 20. xx = xx xx = 22. xx = DDDD = AA DD 21 x + 8 BB 14 CC EE x FF 23. xx = 24. xx = x x 20 Math 2 Unit 6 Review Worksheet
18 25. A student dilates the figure at the right using a center of dilation of (0, 0) and a scale factor of 2. Which statement is true? a) Each angle of the dilated house will be similar but not congruent in the original house. b) Each line segment in the dilated house will be parallel to its corresponding line segment in the original house. c) Some of the line segments of the dilated house may have different slopes than their corresponding line segments in the original house d) The distance between the vertices of a line segment on the dilated house will be 4 times the distance between the vertices of a line segment on the original house. 26. For the triangle at the right, a) Graph the figure representing a dilation of the triangle by a scale factor of 1.5 with the center at (0, 0). b) Should the two triangles be similar? c) Should the corresponding sides be parallel? d) Should the corresponding sides be congruent? e) Should the corresponding angles be congruent? 27. Make a two-column proof. Given: BBBB WWWW Prove: BBBBBB~ DDDDDD Statement Reason Math 2 Unit 6 Review Worksheet
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