NAME: DATE: PERIOD: 1. Find the coordinates of the midpoint of each side of the parallelogram.
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1 NAME: DATE: PERIOD: Geometry Fall Final Exam Review Find the coordinates of the midpoint of each side of the parallelogram. My Exam is on: This review is due on: 2. Find the distance between the two points. Then find the midpoint of the line segment connecting the two points. (5, 3), ( 4, 7) 3. Prove that A(1, 1), B(3, 3), and C(5, 1) are the vertices of a right triangle. 4. has endpoints and Prove that the midpoint of lies in quadrant IV.
2 5. Use the given vertices to graph. Classify. Then find its perimeter. 6. Write an equation in slope-intercept form for the line that passes through and is perpendicular to the line described by. 7. Write the equation of the line that has y-intercept 4 and is parallel to. 8. Suppose the preimage for the transformation given by the rule has vertices,,,,, and. Use the rule to determine the coordinates of the corresponding vertices of the image. Preimage Image
3 9. Rotate this figure the given number of degrees counterclockwise about the origin. List the coordinates of the vertices of the image. S (, ) T (, ) U (, ) V (, ) S (, ) T (, ) U (, ) V (, ) 10. Rotate the figure 90 about the origin. List the coordinates of the vertices of the image. J (, ) K (, ) L (, ) M (, ) N (, ) J (, ) K (, ) L (, ) M (, ) N (, ) 11. The vertices of are, and. Find the vertices of after a composition of the transformation in the order they are listed. Translation: Reflection: in the -axis A (, ) A (, ) B (, ) B (, ) C (, ) C (, ) 12. A triangle with vertices,, and is reflected across the y-axis. Identify the coordinates of the image of point Q. Q (, ) 13. Identify the image of the point when A is reflected across the line. A (, )
4 14. Graph the triangle whose vertices have the coordinates given below. Then draw its reflection in the x-axis. ( 7, 2), ( 2, 2), ( 6, 7) 15. Decide whether the transformation from Figure A to Figure B is a translation, reflection, or rotation. 16. Tell whether a rigid motion can move the solid figure onto the dashed figure. If so, describe the transformation(s) that you can use. If not, explain why the figures are not congruent. 17. Identify the transformation(s) you can use to move figure A onto figure B.
5 18. Determine whether the figure has line symmetry. If possible, identify the number of lines of symmetry. 19. Decide whether the figure has line symmetry and/or rotational symmetry. Identify the number of lines of symmetry and/or the rotations that map the figure onto itself. 20. On the regular hexagon, draw all possible lines across which you can reflect the hexagon onto itself. 21. Find the length of. State the postulate or theorem you use. 22. Given, find the length of all unlabeled sides and the measure of all unlabeled angles. J 4 cm 60 8 cm I K M N cm L
6 23. In the figure below,. Find and m. H T F G S 1.9 R 24. Prove that the triangle with vertices,, is an isosceles triangle
7 Point R lies on the line segment joining P( -7, 8 ) and Q( 5, -4 ). If PR = RQ, what are the coordinates of R? 29. One end of a line segment has the coordinates ( -3, -8 ). If the midpoint is ( 5, 8 ), then what are the coordinates of the other endpoint? 30. Consider the point at. a. Find the coordinates of, the image of after the transformation. b. What type of transformation is? c. Find the coordinates of, the image of after the transformation. d. Write a transformation rule to map to. 31. Use the figure below to answer parts a through c. y c. Is the result from part b the same as the result of translating the x original figure using followed by rotating it 2 by counterclockwise about the origin? Explain your reasoning. 4 6 a. Draw the image of the figure after a counterclockwise rotation about the origin. b. Draw the image of the figure from part a after the translation.
8 32. Find the measure of each of the numbered angles. Explain your reasoning for each angle. D E 110 G F 33. What is the value of a?
9 36. Determine whether the lines are parallel, intersect, or coincide. Make sure to put in y = mx + b form. a. y = 2x + 5 b. y = 1 x y = 2x 1 x 3y = 12 parallel coincide c. y = 5x 2 d. 5y + 2x = 1 x + 4y = 8 parallel y = 2 x + 3ntersect Define circumcenter: 38. Find the circumcenter of each triangle. A. B.
10 39. Determine whether each pair of triangles is congruent by SSS, SAS, or neither. A. B. C. D. 40. Determine whether each pair of triangles is congruent by ASA, AAS, or HL. If they are not congruent, write no conclusion. A. B. C. D.
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