2. For the statement above, write either bi-conditional or give a counterexample.

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1 Name: Hour: Date: / / Geometry - Study Guide for Semester 1 Geometry Exam 1. Read the following statement below and then write the inverse, converse, and contrapositive. If Zach receives a Lego ity set for his birthday, then he will be happy. 2. For the statement above, write either bi-conditional or give a counterexample. 3. Define inductive reasoning. Give an example. 4. Define deductive reasoning. Give an example. Define each of the following terms. Quadrilateral 6. Parallelogram 7. Trapezoid 8. Isosceles Trapezoid 9. Kite 10. Rectangle 11. Rhombus 12. Square 13. Draw the flow chart for quadrilaterals using each of the terms for numbers What is the midpoint formula? Solve the midpoint of the points (, 2) and (8, 3). 1. What is the distance formula? Solve the distance of the points (, 2) and (8, 3). 16. How do you solve the hypotenuse of a triangle? Give an example when both legs of the triangle are equal to Supplementary angles equal how many degrees? omplementary angles equal how many degrees? 18. cos 10 ( ) 19. sin tan( 30 ) 21. sec( 210 ) 22. csc( 40 ) 23. cot( 30 ) For the shape at right, answer the following questions. J (2, 4) K (4, 8) L (4, 3) M (6, 7) 24. Find the slope and length of each side of the shape. 2. Find the slopes and midpoints of the diagonals KL and JM. 26. What shape is shown above.

2 Use the shape below to answer the following questions. P (6, 3) Q (3, ) R (6, 7) S (9, ) 27. Find the slope and distance of each side of the shape. 28. Find the slopes and midpoints of the diagonals PR and QS. 29. What shape is shown above. across the x-y-axis r x=0 resulting image? 30. When the figure is reflected ( ), what are the coordinates of the 31. When the figure is translated using the rule ( x, y) ( x 3, y 7) or T ( 3, 7), what are the coordinates of the resulting image? 32. When the figure is rotated 180 o, what are the coordinates of the resulting image? 33. When the figure is rotated 90 o clockwise, what are the coordinates of the resulting image?

3 34. When the figure is dilated by a factor of 3, what are the coordinates of the resulting image? 3. When the figure is reflected across the y-axis and then translated using the rule (x+8,y), what are the coordinates of the resulting image? 36. What is the rule for the translation of onto?

4 37. What type of rotation maps onto? 38. What type of rotation maps onto? 39. What is the equation of the line of reflection that maps onto?

5 40. Graph the line x = 3. Find a second line of reflection so that the composite of the two reflections will translate D 10 units to the right. Write the composite. y x Reflect over the line y = x and then over the line y = x ( r y= x! r y=x ). 10 y 10 x Fill in the table below. (3, 2) (1, 6) (6, 10) (, ) (, ) (, ) (, ) (, ) (, ) What transformation results from this composite transformation?

6 42. Determine whether the problem below is done correctly or not. If not, identify any mistake(s) and correct it. Given: Line 1 Line 2 x x y y Reflect over 1 line then 2 line ( point ) Distance between Line 1 and Line 2: x + y Distance between Point and Point : Line 1 Line 2 x + x + y + y 2x + 2y 2(2x + y) 43. For the problem below, the bold triangle,, is transformed to its image. Identify type of transformation used. the 44. For the problem below, the bold triangle,, is transformed to its image. Identify the type of transformation used.

7 4. For the problem below, the bold triangle,, is transformed to its image. Identify the type of transformation used. 46. For the problem below, the bold triangle,, is transformed to its image. Identify the composition of transformations used. 47. For the problem below, the bold triangle,, is transformed to its image. Identify the composition of transformations used. 48. For the problem below, the bold triangle,, is transformed to its image. Identify the composition of transformations used.