Unit 5, Day 1: Ratio s/proportions & Similar Polygons
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1 Date Period Unit 5, Da 1: Ratio s/proportions & Similar Polgons 1. If a) 5 7, complete each statement below. b) + 7 c) d) 7 2. Solve each proportion below. Verif our answer is correct. a) 9 12 b) c) A ratio is a of two quantities. Written in three was a. to b. : c., when 0 (wh?) 4. Setting two ratios equal to each other is called a. Form 1: Form 2: means: a c b d a : b c : d etremes: Properties: a) ad bc b) b d a c c) a b c d d) a + b c + d b d 1
2 5. The most efficient wa to solve a proportion is through. 6. Useful applications of proportions: Floor plans, scaled drawings, and maps! 6 cm 3 cm 7 cm 8 cm 3 cm 7. Figures that have the same shape, but a different size are called. a. is the smbol for similar. b. ABC ~ DEF is read triangle ABC is to triangle DEF 8. Which turkes below appear to be similar? Wh or wh not? 9. Two polgons are similar if two conditions are met: a. Corresponding angles are. b. Corresponding sides are. 2
3 10. In the space below, compare and contrast the words congruent and similar. 11. The two figures shown below are similar. Complete congruence and proportion statements below. a) F B C b) D E F c) EF AE BC A G D d) AG FG CD 12. Directions: Determine if the following figures are similar. If the are, write a similarit statement and give the similarit ratio. If the are not, eplain wh. 5. 3
4 Directions: Each pair of polgons below is similar. Find the values of the variables. G P Q A 3.3 ft 5 in. 5 ft F ft E S 8 in. R B 6 ft C L M 3 in. O in N Closure: 1) A student made a drawing on a normal sheet of paper. He wanted to blow it up to poster size he decided that he would enlarge the picture b 5 times. Determine the size of side lengths and angles of the poster. 2) Use the eample above to make a generalization about how enlarging (or shrinking) an image will affect the side lengths and the angles 4
5 Date Period Unit 5, Da 2: Proving Triangles Similar (S. 7-3, p. 382) 13. Name the 5 was ( shortcuts ) that we learned to prove that triangles are congruent. 14. Name both conditions that must be met in order to prove that two polgons are similar. 15. Just like we had shortcuts for congruence, we have shortcuts for similarit. a. Angle-Angle Similarit Postulate (AA ~): If two angles of one triangle are similar to two angles of another triangle, then the triangles are similar Wh are two angles sufficient (not all 3)? b. Side-Angle-Side Similarit Theorem (SAS ~): If an angle of one triangle is congruent to an angle of another triangle and two sides are proportional, then the triangles are similar. c. Side-Side-Side Similarit Theorem (SSS ~): If the corresponding sides of two triangles are, then the triangles are similar. 5
6 Directions: Determine if the triangles are similar. If the are, determine which postulate or theorem ou would use to prove them similar. Directions: Solve for What are the three was to prove that two triangles are similar? 6
7 2. Corollar to Side-Splitter Theorem If three parallel lines intersect two transversals, then the segments intercepted on the transversals are. Eample #3: Solve for and c d 16.5 a b Triangle-Angle-Bisector Theorem: If a ra 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. 3.6 Eample #4: Find the value of A student claims that AB AC below. Describe and correct the student s error. B Triangle angle bisector theorem B BD CD AB AC. Because BDCD, it follows that ABAC. D A C Closure: Compare the Midsegment Theorem (from unit 4) and the Side-Splitter Theorem. How are the related and how are the different? 13
8 Date Period Unit 5, Da 7: Unit 5 Review 1. Find the value of. a. 4 2 b. : 3 12 : 4 7 c Complete each statement below: a. If 3 8, then?? b. If a b, then 7 13 a? b? 3. Assume the figures below are similar. Find the missing values. a. b z 12 z Find the geometric mean between 16 and 25 14
9 5. Use the diagram for the following (these are 3 separate problems): a. KR12, RT9, KS16. Find KT, SU, and KU K b. RT2, KS9, and KU12. Find KR, KT, and SU. R S T U c. RT9, KT36, and KU48. Find KR, KS, and SU. 6. Tell whether the proportion is correct for the diagram shown. If its false, eplain wh! a. d g f e b. f e g d f g d e c. g e f d d. d e f g 15
10 7. Determine which triangles ou need to use (left, right or whole), then show all proportions and solve for each variable a. b z 2 z Graph ABC and TBS with vertices A(-2,-8), B(4,4), C(-2,7), T(0,-4), and S(0,6). Prove: ABC ~ TBS 16
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