6.1 Ratios and Proportions. 6.2 Similar Polygons Review Quiz. 6.3 Proving Triangles Similar. 6.5 Proportions in Triangles
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1 Walczak Math 2 hapter : Similarit ame.1 Ratios and Proportions.2 Similar Polgons.1-.2 Review.1-.2 Quiz.3 Proving Triangles Similar. Proportions in Triangles hapter Review hapter Test ssential Questions: 1. How do ou use proportions to find lengths in similar polgons? 2. How do ou show two triangles are similar? 3. How do ou identif corresponding parts of similar triangles? Important review skills: o Solve equations o Using parallel lines o Finding angles in triangles
2 .1 Ratios and Proportions Ratio: ample 1: bonsai tree is 1 in wide and stands 2 ft tall. What is the ratio of the width of the bonsai to its height? Useful onversions: in = 1 ft 3 ft = 1 d 20 ft = 1 mi 1 oz = 1 lb 0 cm = 1 m mm = 1 cm ample 2: Write the ratio of the first measurement to the second measurement: a) diameter of a table tennis ball: 40 mm b) length of a tennis racket: 2 ft 4 in diameter of a tennis ball:. cm length of a table tennis paddle: in ample 3: The measures of two supplementar angles are in the ratio 1 : 4. What are the angle measures? ample 4: baseball team plaed 14 regular season games. The ratio of the number of games the won to the number of games the lost was : 2. How man games did the win? How man games did the lose? ample : The measures of two supplementar angles are in the ratio : 7. What are the angle measures? ample : The lengths of the sides of a triangles are in the etended ratio 4 : 7 : 9. The perimeter is 0 cm. What are the lengths of the sides? ample 7: The measure of the angles of a triangle are in the etended ratio 4 : 3 : 2. What is the measure of the largest angle? 2
3 Proportion: Properties of Proportions: a b c = is equivalent to: d ample : If =, complete each statement. a. = b. = + c. = d. = ample 9: Solve each proportion. a = b. = c. =
4 .2 Similar Polgons Two polgons are similar if: 1) 2) Similarit Ratio: ample 1: ~FGH. omplete each statement. a. m = b. m = 3 c. F =? F 7 G d. GH = FG? H ample 2: etermine whether the triangles are similar. If the are, write a similarit statement and the similarit ratio. F,, F 4
5 ample 3: Sketch XYZ and MP with X M, Y, Z P. lso, XY =, YZ = 14, ZX = 1, M = 1, P = 21, and PM = 24. an ou conclude that the two triangles are similar? plain. ample 4: a. LMO ~ QRST. Find the value of. O T S L M Q R b. Find SR. ample : Pentagon JKLM ~ Pentagon PQRST. Find each measure. 4 J 0 P 0 1 K T 170 Q M 14 L 1 0 S 130 R 2 a. m = b. m Q = c. M = d. SR =
6 .1-.2 Review 1. FH ~ MLP. Find the missing values below. a. m H = b. = The door in a room is ft tall. n architect s model of the same door is 2 in. high. What is the ratio of the height of the model to the real height? F 3 H P M 74 L 3. Solve each proportion. a. 4 = b. 22 = c = 3 4. If ~ LMO, then: a. m =. b. LO =?. 3-in. b -in picture is enlarged so that the longer side measures ft. What is the length of the shorter side?. re the polgons similar? plain wh or wh not
7 .3 Proving Triangles Similar 3 Was to Prove Triangles Similar 1. ngle-ngle Similarit (~) Postulate ample 1: re these triangles similar? If so, write a similarit statement. 4 4 F 2. Side-ngle-Side Similarit (SS ~) Theorem ample 2: G. re the triangles below similar? If so, write a similarit statement G 3 P K H I 3. Side-Side-Side Similarit (SSS ~) Theorem ample 3: re these triangles similar? If so, write a similarit statement. K 9 J L M O 7
8 ample 4: re these triangles similar? If so, write a similarit statement. P Z Q 3 R X 4 Y ample : re these triangles similar? If so, write a similarit statement. T S 1 U 24 W 1 V ample : Find the value of. The two triangles are similar. ample 7:. Find the length of WY. X W 4 Z Y
9 .3 Practice 1. re the following triangles similar? If so, b what postulate or theorem? If the triangles are similar, write a similarit statement and solve for. If necessar, round to the nearest tenth. a) Given:!S!K S 14 K L H J M b) 1 17 c) Given:!R!S J 9 R S d) Given: TS! R T 2 S G R 9
10 . Proportions in Triangles Side-Splitter Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionall. ample 1: ample 2: Solve for. Solve for. 1 J L M K orollar: If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. ample 3: Solve for and
11 ample 4: The segments joining the sides of trapezoid RSTU are parallel to its bases. Find and. R S. 9 U T Triangle-ngle-isector Theorem: If a segment 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. ample : ample : Find the value of. Find the value of
12 hapter Review #1 4: Solve for. 1. = = = 4. = Find value of and. If necessar, round to the nearest tenth re the triangles similar? If so, b what postulate or theorem? If the are similar, write a similarit statement. 17 F crate is 1. ft. high and casts a 2-ft shadow. t the same time, an apple tree casts an 1-ft shadow. How tall is the tree? Round to the nearest tenth.. scale model of a boat is 9 in. long. The boat s actual length is 0 ft. Find the ratio of the length of the scale model to the length of the boat.
13 9. Find the value of. Round to the nearest tenth When a ft tall man casts a shadow 1 ft long, a nearb tree casts a shadow 93 ft long. How tall is the tree? 11-13: etermine whether the following triangles are similar. If so, state the postulate or theorem that can be used to prove the are similar. Then, write the similarit statement Similar? 30 Thm/Post F Sim. Statement. J K L 9 M Similar? Thm/Post Sim. Statement 13. K Similar? Thm/Post F Sim. Statement 13
14 14. Solve for. 1. Solve for Solve for Solve for and ft building casts a shadow 40 ft long. t the same time, a girl casts a shadow ft long. How tall is the girl? hallenge: The triangles are similar. The area of the smaller triangle is in 2. Find the value of and. 4 in 1 in 14
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