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Chapter 7 Review Name:_____________________________________________ Solve each proportion for x. 1. 2 x 3 15 2. 4. 4 16 9 x 5 3 x x 1 3. 5. x 3 x2 4 15 6 x2 Are the triangles similar? If so, pick the statement you can use to prove they are similar. a) two angles of one triangle are congruent to two angles of another triangle b) an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional c) the corresponding sides of two triangles are proportional 6. yes or no _________ Why (if yes) _________ 7. yes or no ___________ 8. yes or no __________ Why (if yes) _________ Why (if yes) _________ The figures in each pair are similar. Find the value of each variable. 9. x = __________ 10. x = ___________ y = _____________ z = _____________ 11.. These triangles are similar. Finish the similarity statement. Triangle XYZ ~ ___________ 12. A meter stick is held perpendicular to the ground It casts a shadow 1.5 m long. At the same time, A telephone pole casts a shadow that is 9 m long. How tall is the telephone pole? 13. A photographic negative is 3cm by 2cm. If a similar print from the negative is 9 cm on its shorter side, what is the length of its longer side? 14. A video screen is 20 in. wide by 15 inches tall. A picture that is 4 inches wide by 2 inches tall is to be magnified to fit on the screen. What is the largest complete image size possible for the screen? 15. A map scale of 1 inch : 30 miles is used for a map of Colorado. If the distance from Fort Collins to Castle Rock is 3 inches, what is the actual distance from Fort Collins to Castle Rock? Find the geometric mean. If the answer is not a whole number, leave it in simplest radical form. 16. 8 and 12 17. 2 and 6 Use the figure at the right to complete the proportions. 18. JR MW ? WL JP ? SQ QL 19. 20. KM ? KL LW Find the value of x. Leave answer in radical form, if needed. 21. x = _________________ 22. x = ______________ 23. x = _____________________ 24. y = ______________ 26. x = _______________ 25. x = ________________ 27. x = ________ 28 x = ___________ y = _______________ z = ________ 29. In the diagram, explain how you know that RZS ~ TZW 30. Factor completely. a) x 36 2 b) 10 x 45 x 90 2 31. Solve for x, using the quadratic formula. 8x 2 2x 3 0 c) x 6 x 27 2