Unit 5b/Chapter 6: Similarity Name: Block:
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1 Unit 5b/hapter 6: Similarity Name: lock: SOL G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods. Page 1 of 20 lock / ate 1 Section and Objectives 6.1 Ratios, Proportions, and the Geometric Mean Simplify ratios with like units Simplify ratios with unlike units Use ratios to find the dimension of an object Solve problems involving extended ratios Solve proportions Find the geometric mean of two positive numbers lasswork and Homework Pg 360 #3, 7, 21, 22, 26, 29, 31, 35, 41, 42, 61, 64 Pg 367 #3, 6, 11,, 16 WS Practice Use Proportions to Solve Geometry Problems pply the dditional Properties of Proportions Use proportions to solve problems with geometric figures 6.3 Use Similar Polygons Use similarity statements to identify pairs of congruent angles and/or corresponding sides in figures Write proportions for similar figures and determine missing side lengths etermine the scale factor for a given set of polygons For similar polygons: the ratio of corresponding lengths = scale factor = ratio of perimeters 6.4 and 6.5 Prove Triangles Similar by ~, SSS~, and SS~ etermine if two triangles are similar by ~, SSS~, or SS~ Similar Figures lue/grey Partner ct WS re Figures Similar (pg 257) WS Finding Sides of Similar Figures (pg 258) Pg 376 # 1, 6, 9, 20 WS: Review Quiz next class on Proving Triangles Similar hart Pg 384 # 3 8, 11 13, 16, 20 WS ongruent Triangles and Similar Triangles (pg 39) WS pplying ~, SSS~, SS~ (pg 265) Pg 400 # 3, 4, 8 11, 13 15, 17 Pg 422 #1-13 Test in 2 classes! 6.6 Use Proportionality Theorems Know, apply, and recognize the Triangle Proportionality Theorem Know, apply, and recognize the onverse of the Triangle Proportionality Theorem Set up correct proportions when three parallel lines intersect two transversals Set up correct proportions when a ray bisects an angle of a triangle Test Review Group practice test calculate your score Test Pg 430 #1- Post-test reflection (online) U6 Pre-Test (online) WS Processing ~, SSS~, SS~ (pg 264) Group Practice Test
2 Page 2 of 20 PROVING TRINGLS R SIMILR Postulate/ Theorem ngle ngle Similarity Postulate SSS Similarity Theorem SS Similarity Theorem What it says dditional conclusions See page 390 of your text
3 Page 3 of 20 QR odes for Video Lessons Part Part Part Watched Lesson Notes complete WSQ W/HW Points arned 6.1 U5b Pre-Test U5b Post-Test U6 Pre-Test Review hecked Key Online Groupwork Unit 5b Test Review Test hecked key online Helpful Hints e responsible: watch the videos for each section before coming to class! Review your notes daily. e sure they are accurate, neat, and organized. Pay attention to the details This includes notation, how your work is organized, things I say in class or on a video. ome to class with specific questions.
4 Page 4 of 20 Notes 6.1 Ratios, Proportions, and Geometric Mean ratio of a to b a b or a : b (must be in lowest terms) Simplify the ratio m : 6 m 2. 5ft 20in yards to 3 yards cm : 6 m 5. The measures of the angles in are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. 6. The perimeter of a room is 48 feet and the ratio of its length to its width is 7 : 5. Find the length and width of the room. 7. triangle s angle measures are in the extended ratio of 1 : 3 : 5. Find the measures of the angles.
5 Page 5 of 20 proportion To solve a proportion: 1. cross multiply 2. solve for the variable Simplify. 5 x y 1 3y x x 3 3x. y 3 y x 3 4x Geometric Mean x = Find the geometric mean of the two numbers and and and and 18 WSQ 6-1
6 Page 6 of 20 WS Practice 6.1 Simplify the ratio. 1. $ : $ in. 8in in. 2ft Find the ratio of the width to the length of the rectangle. Then simplify the ratio cm 6 in. 1 ft cm 10 in. 18 in. 7. The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6 : 1. Find the length and the width. 8. The area of a rectangle is 525 square centimeters. The ratio of the length to the width is 7 : 3. Find the length and the width. The measures of the angles of a triangle are in the extended ratio given. Find the measures of each angle of the triangle : 7 : : 6 : : 14 : 15
7 Page 7 of 20 Solve the proportion. 4 x y 14. x x x y 5 y k 1 3k 4 Find the geometric mean of the two numbers and and and and and and 13 Let x = 6, y = 3, and z = 2. Write the ratio in simplest form. 2x y 4z x 26. z 2y 2x 4 Solve the proportion. x 27. x y 2 2y k 2 k 2 4
8 Page 8 of 20 Notes 6.2 Using Proportions dditional Properties of Proportions If a c, b d then b d a c. If a c b d, then a b c d. If a c b d, then a b c d b d. x: 1. In the diagram, MN NP. Write four true proportions. RS ST M 8 N 4 R 10 S x P T 2. In the diagram,. Find and. 18 x scale drawing 3 6 scale 3. You buy a 3- scale model of the Reunion Tower in allas, TX. The actual building is 560 feet tall. Your model is 10 inches tall, and the diameter of the dome on your scale model is about 2.1 inches. a. What is the diameter of the actual dome? b. bout how many times as tall as your model is the actual building?
9 Page 9 of 20 Notes 6.3 Using Similar Polygons similar polygons written as: x: 1. In the diagram, RST ~ XYZ. a. List all the pairs of congruent angles. b. heck that the ratios of corresponding side lengths are equal. 25 T 30 X 15 Z 18 Y R 20 S c. Write the ratios of the corresponding side lengths in a statement of proportionality. 2. etermine whether the polygons are similar. If they are, write a similarity statement and find the scale factor of ZYXW to FGHJ. G 20 F J 25 H Y Z W 15 X 3. In the diagram, F ~ MNP. Find the value of x. N 9 x 20 F M 16 P
10 Page 10 of 20 Perimeters of Similar Polygons: If KLMN ~ PQRS, then KL LM MN NK KL LM MN NK. PQ QR RS SP PQ QR RS SP 4. In the diagram, ~ FGHJK. a. Find the scale factor of FGHJK to. 10 F 15 G 9 b. Find the value of x. x 18 H K 15 J c. Find the perimeter of. 5. In the diagram, TPR ~ XPZ. Find the length of the altitude PS. T 6 S 6 R P 20 X 8 Y 8 Z 6. town is building a new swimming pool. n 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. a. Find the scale factor of the new pool to an Olympic pool. b. Find the perimeter an Olympic pool and the new pool. WSQ 6-3
11 Page 11 of 20 WS Review The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of the triangle : 3 : : 5 : : 3 : 5 Solve each proportion x x x 3 2x x x 2 x x 8 x 3 Find the geometric mean of the two numbers and and and Use the diagram and the given information to find the unknown length. NJ NL 13. Given, find NK. 14. Given, NK NM F N 10 6 J K find. 8 L M F
12 Page of 20 In the diagram, PQR LMN. 15. Find the scale factor of PQR to LMN. 16. Find the values of x, y, and z. P 15 Q y L x z M R 13 N 17. Find the perimeter of each triangle. F. Identify the dotted special segment and find the value of x F 4x x x x F
13 Page 13 of 20 Notes Proving Triangles Similar by, SSS, and SS ngle-ngle () Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. K X L Y Z J Side-Side-Side (SSS) Similarity Theorem If the corresponding side lengths of two triangles are proportional, then the triangles are similar. R If,then~ RST. RS ST TR S T Side-ngle-Side (SS) Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar. X M If ZX XY X M and, then XYZ ~ MNP. PM MN Z P Y N x: 1. etermine whether the triangles are similar. If they are, write a similarity statement. 26 H 64 Show that the two triangles are similar. Then write a similarity statement. 2. and 3. F and F G K F 58
14 Page 14 of flagpole casts a shadow that is 50 feet long. t the same time, a woman standing nearby who is five feet four inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot? 5. Is either F or GHJ similar to? F H J 16 G 6. Find the value of x that makes ~ F. 4 8 x (x + 1) F 7. Tell what method you would use to show that the triangles are similar WSQ
15 Page 15 of 20 Notes Using Proportionality Theorems Triangle Proportionality Theorem Q T If TU QS, then RT RU. TQ US R S U onverse of the Triangle Proportionality Theorem If RT RU, then TU QS. TQ US Q T R S U x: 1. In the diagram, QS UT, RS = 4, ST = 6, and QU = 9. What is the length of RQ? U 9 Q R 4 S 6 T 2. Find the length of YZ. V 35 W 44 X Y 36 Z
16 Page 16 of 20 opy down the theorems that are on page 398 of your text below. Theorem UW WY VX XZ U W Y V X Z Theorem 3. In the diagram, QPR RPS. Use the given side lengths to find the length of RS. Q 7 P 13 R 15 x Find the length of S
17 Page 17 of 20 Unit 5b/hapter 6 Practice Test Group Members: Simplify each ratio cm 4cm ft 30in Solve each proportion. Show all steps x 2 8 3x Use the diagram and the given information to find the unknown length. 5. Given:. Find. 6. Given: JM ML. Find PS. PS SR
18 Page 18 of a) etermine whether the polygons are similar. b) Write a similarity statement if they are. c) Find the scale factor if they are etermine if the triangles are similar by ~, SSS~, or SS~. If they are similar, then write a similarity statement. If they are not similar, write NOT SIMILR...
19 Page 19 of 20 Find the value of x for each problem. Show all work
20 Page 20 of Given: The perimeter of a rectangular field is 440 meters. The ratio of the length to width is 7:4. a) raw a picture to represent the situation. b) etermine the length and width. c) etermine the area of the field. 14. The extended ratios for a triangle are 4:5:11. Find the measure of each angle. 15. Find the geometric mean between 4 and 64. etermine Your Scores: On your own: I earned Possible 16. omplete Page 422, # heck your answers online. 18. Study for the h 6 Test next class. Pg 1 17 Pg 2 14 Pg 3 Pg 4 21 My Score: 64 x 100 = (Total) Team verage:
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