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Geometry Chapter 7 Test Name ___________________________ Solve each proportion for x. 1. 10 5 x 14 2. x 3 8 19 3. x 2 x 1 5 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 4. yes or no _________ Why (if yes) _________ 5. yes or no ___________ Why (if yes) _________ 6. yes or no __________ Why (if yes) _________ The figures in each pair are similar. Find the value of each variable. 7. x = _________ y = __________ 8. x = ___________ y = ____________ 9. These polygons are similar. Finish the similarity statement. ABC ~ __________________ 10. A man 6 ft tall casts a shadow 4 ft long. At the same time, a building casts a shadow 20 ft long. How tall is the building? 11. A video screen is 16 in. wide by 12 in. tall. What is the largest complete video image possible for a block of text that is 3 in. wide by 5 in. tall? 12. A map uses the scale 1 cm = 20 mi. A county is 90 mi wide. How wide is the county on the map? Find the geometric mean. If the answer is not a whole number, leave it in simplest radical form. 13. 3 and 27 14. 10 and 18 Use the figure at the right to complete the proportion. 15. a d b ? ? = _________ 16. f c ? b 17. a ? bc e f ? = _________ ? = _________ Find the value of x. Leave answer in radical form, if needed. 18. x = ___________ 21. x = ___________ 24. x = _______ 19. x = _________ 20. x = ___________ 22. x = ________ 23. x = _________ Find the values of the variables. 25. x = _______ y = _______ z = _________ 26. In the diagram below, explain how you know that ABC ~ EDC. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ Factor. 27. x2 – 49 28. x2 + 5x – 24 29. Solve using the quadratic formula. x2 + 4x – 4 = 0 Extra Credit: Find the value of x.