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Name _________________________________________________ Date ________________ Write each ratio in simplest form. 1. 36: 12 2. 6π₯π¦ 2 3. Ms. Lorenz has 84 students in Geometry. If the ratio of girls to boys is 7:5, find the number of boys. 24π₯π¦ Solve for each variable. 4. 6. π¦β2 2 π₯ π₯β6 = π¦+3 = π₯+5 4 π₯ 5. 7. 5π₯β2 3 β9π¦ π¦+8 = = 7π₯ 4 π¦β3 2 Given the ratio, solve for x. 8. DO : OG : DG is 5 : 5 : 4 9. AC : BC : AB is 2 : 1 : 2 9. The batting average is the ratio of the number of hits to the numbers of at bats. A baseball player with 512 at bats needs how many hits to have a batting average of at least 0.275? Express your answer as a whole number. 10. Find the angle measures for a triangle if the extended ratio of the angles is 17 : 8 : 5. 11. The perimeter of βHIJ is 33. The extended ratio of the sides is 2 : 4 : 5. Find the length of each side of the triangle, then classify the triangle by its sides. 12. The ratio of the measures of two supplementary angles is 7:2. Find the measures of the angles. 13. Find the scale factor of Figure A to Figure B. 14. Find the scale factor of Figure B to Figure A. 14 24 B 36 20 20 A A 9 12 21 B 28 25.2 15 15. If βNML ~ βSRL, find the value of x. R M 28 24 L 3x β 1 x+7 S N 16. If βDEF ~ βJKL, find KL. L E 10 D x + 11 6x + 3 F J 25 K 18 Determine if the triangles are similar, if possible, by AA~, SAS~, or SSS~. Show all work to support your answer. 7 17. 18. 37Λ 28Λ 125Λ 125Λ 39Λ 4 27Λ 6 11 15Λ 129Λ 19. 20. 5 14 24 15 27 18 18 21 16.5 5.5 Write a proportion and solve to find the value(s) of the variable(s). (Drawings may not be drawn to scale) 21. 22. 23. 24. 25. Find the value of x. The figure is not drawn to scale. Round your answer to the nearest tenth. 40 ft 5.5 ft x 8 ft 26. Complete the following proof: Given: β ADC and β BEA are right angles Prove: βADC ~ βAEB Statements Reasons 1. 1. 2. 2. 3. 3. 4. 4.