H Geo Final Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 H Geo Final Review Packet Multiple Choice Identif the choice that best completes the statement or answers the question. 1. Which angle measures approximatel 7?.. In the figure below, what is the name of the angle formed b ras and? What is the common endpoint for this angle? S T Q R P ; ; ; ; 5. In the figure below, identif two line segments that are portions of a pair of lines that appear to be parallel.. Which is NOT a possible value for in the figure below? K B A C D J F Which of the following describes a major difference between parallel lines and perpendicular lines? Parallel lines intersect at either obtuse or acute angles, and perpendicular lines intersect at right angles. Parallel lines intersect, and perpendicular lines do not intersect. Parallel lines do not intersect, and perpendicular intersect. Parallel lines intersect at right angles, and perpendicular lines intersect at either obtuse or acute angles. and and and and. A quadrilateral with vertices,,, and is reflected across the -axis. Which is NOT a vertex of the image? H Not here G

2 7. Which point is the image of reflected across the -axis? 11. Which coordinate notation correctl describes a transformation that maps the black triangle to the gra triangle? 8. Which mapping represents a rotation of clockwise about the origin? 9. is shown below. Suppose the triangle is translated 5 units to the right and 7 units down. What are the coordinates of the image of vertex after this transformation? The rotation The translation The rotation The translation 1. Which figure has rotational smmetr? 10. Which transformation rule below translates points 5 units to the left and units up? 13. Which of the following capital letters is a reflection image of itself across a horizontal line? M N O P

3 1. Which rotation about point P maps C to H? 17. Reflecting over which line will map the trapezoid onto itself? CCW CCW CCW CCW 15. A reflection of the rectangle over which line will map the rectangle onto itself? = 1 x = 1 = 0 x = WXYZ is a trapezoid with vertices W( 1, ), X(3, ), Y(5, 1), and Z( 3, 1). Which is a line of smmetr with the correct justification? because it connects the midpoints of and. because it connects the midpoints of = 0 = 1 = x = x 1. Reflecting over which line will map the rhombus onto itself? and. Both choices A and B are lines of smmetr. ABCD has no lines of smmetr. 19. ABCD is a trapezoid with vertices A( 3, ), B(, 5), C(8, ), and D(, ). Which is a line of smmetr with the correct justification? because it connects the midpoints of and. because it connects the midpoints of and. Both choices A and B are lines of smmetr. ABCD has no lines of smmetr. = x = x = 0

4 0. Which transformation will create an image of MNOP that coincides with the original figure? 3. Determine which of the following transformations maps the given figure onto itself. N O Q M P 7 A reflection across the diagonal MO. A 180 clockwise rotation about point Q. A reflection across the side MN. A 90 counterclockwise rotation about point Q. 1. Which transformation will create an image of trapezoid QRST that coincides with the original figure? Reflection across a vertical line Reflection across a horizontal line rotation CCW rotation CCW. How man lines of smmetr does a square have? Q R ( 5, ) ( 3, ) S (3, ) T (5, ) x Which transformation does NOT appear to be a rotation? A 180 clockwise rotation about the origin. A reflection across the axis. A reflection across the x axis. A 90 counterclockwise rotation about the origin.. Point G is the midpoint of segment, and point H is the midpoint of segment. Which transformation(s) will create an image of the regular hexagon ABCDEF that coincides with itself? A G B F C. Which tpe of transformation maps to? E H D Reflection across the line. Rotation of 90 degrees about the center of the hexagon. Rotation of 70 degrees about the center of the hexagon. Reflection across the line. Rotation Reflection Translation Dilation

5 7. Which mapping represents a rotation of about the origin? clockwise 8. A person facing east walks east 0 paces, turns, walks north 10 paces, turns, walks west 5 paces, turns, walks south 10 paces, turns, walks east 15 paces, and then stops. What one transformation could have produced the same final result in terms of the position of the person and the direction the person faces? reflection over the north-south axis rotation translation reflection over the east-west axis 9. Which statement describes the image? Reflection in the line Rotation of about point Rotation of about the origin Translation right two units, down units 30. After a transformation, the image of is. The segments,, and are not parallel. What tpe of transformation could this be? a reflection a rotation a translation not enough information is given 31. Triangle JKL with coordinates J(, ), K( 1, ), and L(3, 0) is reflected over and then that image is reflected over. Which phrase best describes the final image after these two transformations? a reflection of over a rotation of about K a reflection of along a vector parallel to the original 3. When is reflected over to produce, which statement will not necessaril be true? FP F P 33. What is a definition of a reflection of a preimage point across line? If a point is on line, then is the perpendicular bisector of, where is the image of. If is not on line, then. If a point is on line, then, where is the image of. If is not on line, then is the bisector of. If a point is on line, then, where is the image of. If is not on line, then is perpendicular to. If a point is on line, then, where is the image of. If is not on line, then is the perpendicular bisector of. 3. What is a definition of a translation of a point b a vector? A transformation such that the segment joining and its image has the same magnitude as and is parallel to. A transformation such that the segment joining and its image is parallel to. A transformation such that the segment joining and its image has the same magnitude as. A transformation such that the segment joining and its image has the same magnitude as and is perpendicular to. 35. What is a definition of a rotation of about a point? A transformation where if a point has image, then has a measure of. A transformation where ever point and its image are the same distance from and if a point has image, then has a measure of. A transformation where ever point and its image are the same distance from the origin O and if a point has image, then has a measure of. A transformation where ever point and its image are the same distance from P and if a point has image, then has a measure of, where is the origin.

6 3. Polgon,, was mapped to polgon,,. First b the dilation: translation?. And then b which 37. The preimage for a reflection is shade Which represents the mapping? 0. Which picture shows a reflection of the flag? 38. with vertices,, and is reflected across the -axis, and then its image is reflected across the line. Which single transformation moves the triangle from its starting position to its final position? rotation b CCW about the origin rotation b CCW about the origin reflection across the x-axis reflection across the -axis 39. Which are the angle of rotation and the order of rotational smmetr for the figure? 1. Which graph represents a reflection in the -axis? ; ; ; ;

7 . Draw the image of the figure under a translation x Draw the image of the figure after a reflection across the. x x 8 8 x 8 8 b. 8 8 x x 8 8 x 8 8 x x x 8

8 . Draw the image of the figure after a counterclockwise rotation about the origin. x x x x 5. Describe the transformation ou can use to move the solid figure onto the dashed figure. x reflection dilation translation rotation

9 . Draw an example of the effect of rotation on the solid figure. 7. Given a triangle with vertices,, and, which points represent a reflection of in the -axis?,,,,,,,, 8. If, which segment is congruent to? 9. If, what is the length of? B H A 10 C G I The length cannot be determine 50. Which CANNOT be used to justif the statement? SSS SAS AAS ASA

10 51. What information is needed to prove SAS? b 55. Which of the following can be concluded given? t 5. Wh is there no congruence relationship for all three angles (AAA) of a triangle? Triangles with three identical angles are never congruent. To show the congruence of two triangles, onl two angles at most need to be known. Triangles with congruent corresponding angles are the same shape, but ma not be the same size. To show the congruence of two triangles, onl one angle and the length of one side, at most, need to be known. 53. Which of the following transformations does NOT represent a rigid motion? ( x, ) ( x, ) ( x, ) ( 3 x,3) ( x, ) ( x, + ) x, x, ( ) ( ) 5. Given,, and, which is a good first step when proving that? Find a sequence of rigid motions that maps onto. Find a sequence of rigid motions that maps onto. Find a sequence of rigid motions that maps onto. Translate so it maps onto m XYW = and is the image of after a reflection across line. What is true about as a result of this reflection? Y 3 5 m XYZ = m XYW = m WYZ is a right angle. is an obtuse angle. 57. Given, Miguel is proving. He has drawn auxiliar line l, parallel to. Which of the following congruencies is likel to be part of his proof? S X Z W p q m l R 1 Q

11 58. Given, Anna is proving. Which statement should be part of her proof? N 0. You are given the coordinates of points AB,, and C and want to use a coordinate proof to prove that, the midsegment of, is parallel to. Which is the best first step? B E M In the proof shown here, what is the correct reason that can be used for Step and Step 3? Z 3 P A D Use the midpoint formula to find the coordinates of points Dand E. Use the distance formula to find the length of DE. Use the slope formula to find the slope of DE. Use the slope formula to find the slope of AC. C Y X 1. Quadrilateral RSTU is a parallelogram. Which is the LEAST additional information needed to prove that RSTU is a rectangle? Given: Prove: Statement Reasoning Given The sum of the interior angles in a triangle is. If two sides of a triangle are congruent, then the angles opposite the sides are congruent. If two angles of a triangle are congruent, then the sides opposite the angles are congruent. SSS congruence criterion Both pairs of opposite sides are congruent, and all angles are right angles. All four angles are right angles. The diagonals are congruent, and one angle is a right angle. is a right angle.. KLMN is a square and. Which can be proved?

12 3. Given: ABCD is a parallelogram,, and AB BC. Conclusion: ABCD is a square. What can be said about the conclusion?. Given and, what triangle congruence criterion is likel to be used in a proof that and? B C Valid Not valid. Which information is sufficient to prove that quadrilateral ABCD is a parallelogram? The diagonals bisect each other. and are supplementar. 5. The first part of a proof is shown below. What is a valid reason for Step? A Given: Prove: and and SSS ASA AAS SAS 7. Which of the following best describes the construction? B D Given: ABCD is a parallelogram with diagonal. Prove: B C P Q A D A is the perpendicular bisector of. Statement Reasoning 1. Definition of parallelogram. Definition of parallelogram When parallel lines are cut b a transversal, alternate interior angles are congruent. When parallel lines are cut b a transversal, corresponding angles are congruent. Corresponding parts of congruent triangles are congruent. is perpendicular to. is perpendicular to. is the perpendicular bisector of. 8. Which of the following best describes the construction? m A C D is the midpoint of m. C is the midpoint of m. B D

13 9. For a coordinate proof concerning an isosceles triangle, which coordinates might be easiest to use? (0, 0), (a, 0), (a, b) (0, 0), (a, b), (a, b) (a, a), (b, b), (c, c) (a, b), (c, d), (e, f) 70. Given: TUVW is a rectangle. Prove: Which set of coordinates could ou use to do a coordinate proof?,,,,,,,,,,,, 71. Which of the following sets of points are vertices of a right triangle?,,,,,,,, 7. Which angle in the quadrilateral with vertices,,, and is a right angle? 73. Which of the following equations describes a line parallel to the line graphed below? 7. Which of the following equations describes a line passing through that is perpendicular to the line described b? 75. Which equation describes the line that passes through and is parallel to the line described b? 7. Which equation describes a line parallel to the line described b? 77. Which equation describes a line that passes through and is perpendicular to the line described b? 78. Which equations describe parallel lines? I. x+ 3 = 15 II. 3x = 8 3 III. + 1 = ( x ) IV. = x 5 3 I and II I and III II and IV III and IV

14 79. Which equation describes a line that is NOT parallel to the lines described b the other three equations? I II III IV I II III IV 80. Which equation describes a line that passes through and is perpendicular to the line described b? 81. Which pair of lines is perpendicular? 8. Which equation describes a line that is parallel to the line described b? 83. Which equation describes a line that passes through (7, 1) and is perpendicular to the line described b? 8. Which equation represents the graph of the line that coincides with the graph of? 85. The graph of which equation is parallel to the line in the graph? 8. The graph of which equation is perpendicular to the graph of? 87. A line passes through the points and. What is the slope of a line that is parallel to that line? 88. What is the -intercept of a line parallel to that passes through the point 9

15 89. Find the area of a triangle with vertices A(0, ), B(8, ), and C(, 3). 17 square units 0 square units 15 square units 19 square units 90. has vertices and has an area of 10 square units. Which is NOT a possible location for the third vertex? 91. What is the perimeter of, rounded to the nearest whole number? 93. Refer to the figure shown. Which of the following statements is true? 9. Given: with. Which statement of congruence is not provable? 95. The figure shows the paths through a park. Which justifies the statement? 19 units 3 units 30 units 33 units 9. is an altitude of. What is the exact area of? SAS SSS ASA HL 9. Which conclusion can be drawn from the given facts in the diagram? 75 square units square units 150 square units square units bisects.

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