PARCC Review. The set of all points in a plane that are equidistant from a given point is called a

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1 Name 1. Select the drop-down menus to correctly complete each sentence. PARCC Review The set of all points in a plane that are equidistant from a given point is called a The given point is called the Radius Area Center Perimeter 2. Select from the drop-down to correctly complete each sentence. Given distinct noncollinear points A, B, and C, the set of all points between A and C including A and C is 3. Which geometric figures have a measurable quantity? Select each correct answer. A. line B. angle C. point D. line segment 4. Using a compass and a straightedge, a student constructed a triangle in which XY one is one of those sides. The compass is opened to a set length and two intersecting arcs are drawn above XY using X and Y as the centers. The intersection of the two arcs is labeled as a point Z. Part A What could be the set length of the compass so that is triangle XYZ isosceles but not equilateral? Select all that apply A. less than ½ XY B. equal to ½ XY C. between ½ XY and XY D. equal to XY E. greater than XY Select the correct phrase to complete the sentence If the opening of the compass is then XYZ will be equilateral 1

2 5. Jericho is making several constructions based on the segment shown. Part A For his fist construction, Jericho made the markings shown with a compass open to a less than the length of segment PQ. Jericho s markings are useful for the construction of which of the figures listed? Select all that apply A. a 60 angle B. a bisector of PQ C. line perpendicular to PQ D. a rhombus with PQ as one diagonal E. an equilateral triangle with side PQ The first steps of Jericho s second s construction are shown. After drawing arcs from point S and point R, he adjusted the compass length using the intersection of the arc from point S with PQ and SR. Which figure is he constructing? A. the bisector of PQ through point R B. an angle congruent to RPQ with vertex R C. a line through point R that is parallel to PQ D. a circle containing points P, Q,and R 2

3 6. Quadrilateral ABCD is shown graphed in the xy- coordinate plane. Part A Quadrilateral ABCD will be translated according to the rule (x, y) (x + 3, y 4) to form A B C D. Select the correct orientation of A B C D and place it correctly on the plane. Quadrilateral ABCD maps onto A B C D.It will undergo a different transformation that will map. A( 6,3) to A, B(-4,5) to B, C (-1,6) to C, and D (-3,2) to D.The transformation will consist of a reflection over the y-axis followed by a translation. Point D is shown plotted in the plane after the transformation. Plot the point A in the plane. 3

4 7. Part A Line l passes through the (-4,-7) and (2, -3) points on the coordinate plane. Line m passes through the points (-4,1) and (2,w). For what value of w is line m parallel to line l? Enter your answer in the box. Given the figure, write the expression that can replace t and will guarantee that lines j and k are parallel. Support your answer. 4

5 8. The diagram shows regular hexagon ABCEF with center at O. Justine made these claims. The only lines of symmetry for regular hexagon ABCDEF are the lines that contain one vertex and O. The only angle of rotation that shows rotational is 120 Explain why Justine is correct or incorrect. Enter your explanation is the space provided. 9. Triangle JKL will undergo a transformation to create triangle J K L in the xy- coordinate plane. Which transformations will result in JKL J K L" A. (x,y) (-x,-y) B. (x, y) (-x,y) C. (x, y) (x, y - 5) D. (x, y) (x + 3, y 5) E. (x, y) (2x, 3y) F. (x, y) (-x, y + 3) 5

6 10. In the figure, p ǁ q. Transversals t and intersect at point L. Part A What is the missing reason in step 3? A. Alternate interior angles along parallel lines are congruent. B. Alternate interior angles along parallel lines are congruent. C. Corresponding angles along parallel lines are congruent D. Vertical angles are congruent Consider the proof of p q given that LHK ~ LJZ. If LHK ~ LJZ, then LHK LJZ, because corresponding angles in similar triangles are congruent. Which statement concludes the proof? A. If LHK LJZ then p q because when base angles are congruent, the lines are parallel. B. LHK LJZ then p q because when corresponding angles are congruent, the lines are parallel C. If LHK LKH then p q because when alternate exterior angles are congruent, the lines are parallel D. If JLZ HLK, then p q because when corresponding angles are congruent the lines are parallel 11. Triangle ABC is shown in the xy- coordinate plane. The triangle will be translated 2 units down and 3 units right to create triangle A B C. Indicate whether each of the listed parts of the image will or will not be the same as the corresponding past in which the preimage (triangle ABC) by selecting the appropriate box in the table. 6

7 12. The right triangle in the coordinate plane is rotated 270 clockwise about the point (2, 1) and then reflected across the y- axis to form triangle A B C. Drag and drop the appropriate orientation for triangle A B C into the correct position on the coordinate plane (sketch it). 13. Triangle ABC is graphed in the xy- coordinate plane, as shown. Part A Triangle ABC is reflected in the x- axis to form triangle A B C. What are the coordinates of C after the reflection? A. (-6, 4) B. (3, -2) C. (4, -6) D. (6, -4) Triangle ABC in the xy- coordinate plane will be rotated 90 degrees counterclockwise about point A to form triangle A B C. Which graph represents A B C? 7

8 14. An incomplete proof of the theorem that the sum of the interior angles of a triangle is 180 degrees is shown. Part A What is the appropriate reason for the statement in step 1? o A. Through any two points, there is exactly one line o B. Though a point not on a line. There is exactly one line parallel to the given line o C. If two lines cut by a transversal form congruent corresponding angle, then the lines are parallel. o D. If two lines cut by a transversal form congruent alternate interior angles, then the lines are parallel. Which pairs of angles congruence or equalities should be used for the statement in step 2? Indicate all such pairs. A. 1 2 or m 1 = m 2 B. 1 3 or m 1 = m 3 C. 1 4 or m 1 = m 4 D. 1 5 or m 1 = m 5 E. 2 3 or m 2 = m 3 F. 2 4 or m 2 = m 4 G. 2 5 or m 2 = m 5 H. 3 4 or m 3 = m 4 Part C Select from the drop down menu to correctly complete the sentence. The reason for the statement in step 2 is that Part D Select from the drop down menu to correctly complete the sentence. The appropriate reason for the statement in step 5 is the 8

9 15. Octagon PQRSTVWZ is a regular octagon with its center at point C. Which transformations will map octagon PQRSTVXZ onto itself? Select each correct transformation A. reflecting over QV B. reflecting over RW C. reflecting over TZ D. rotating 45 clockwise around point Z. E. rotating 135 clockwise around point C F. rotating 90 counterclockwise around point C. 16. Part A ABC meets the given criteria The perimeter of ABC is 50 units, Only two of the sides have the same length The third side is 16 units long, given in the diagram What are the coordinates of point C that will meet the criteria for ABC? o A ( 6.25,8 ) o B ( 8, 6.25 ) o C ( 8, 15 ) o D ( 15, 8 ) Point C is placed at (12, 16) and point B is moved along the x-axis. Triangle ABC is still an isosceles triangle and point A is still at the origin. What is the new perimeter of ABC? Provide valid mathematical reasoning and calculations to support your answer. Enter your answer, your reasoning, and your calculations in the space provided 9

10 17. Given: In triangle ABC shown, Part A Select from the drop down menus to correctly complete step 2 of the proof. Select from the drop down menus to correctly complete step 4 of the proof. Part C Select from the drop-down menus to correctly complete step 5 of the proof. because of Part D What is the correct reason for the statement in step 6? A. The transitive property of congruence B. base angles of isosceles triangles are congruent C. corresponding parts of congruent triangles are congruent D. vertical angles are congruent 10

11 18. In the diagram, quadrilaterals FBAG and CDEF are rectangles How long is DE rounded to the nearest tenth? Enter your answer in the box. HINT label what you know and then look for similar triangles. 19. Triangle ABC has sides with lengths of 3, 6 and 8. Classify each of the transformations described as producing a triangle similar to triangle not similar to triangle ABC. Drag and drop each transformation into the appropriate box (use the numbers 1-4):

12 20. Point A is located at -3, and point B is located at 19. Select a point on the number line between A and B such that the distance from A to the point is 3/11 of the distance from A to B. Select a place on the number line to plot the point. 21. A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the screen to the height of the screen, is 16:9. What is the length of the diagonal of the screen, to the nearest whole inch? Enter your answer in the box 22. In the xy- coordinate plane shown, line l passes through point C and has a slope of -2. A dilation of line l with center A and a scale factor of 3 will produce a new line through point C, the image of point C with coordinates (, ) and with a slope of 12

13 23. Triangle P is dilated from center A by a scale factor of 2 to form triangle Q. The vertices from triangle P are (-2,1), (2,4) and (2,1). The vertices for triangle Q are (-1,-3), (7,3) and (7,-3). Graph point A, the center of the dilation. Select the point on the coordinate plane. 24. Triangle ABC is dilated from the center A by a factor not equal to 1 to form triangle AKL. Which of the statements must be true? Select all that apply. A. AB and AK line on the same line B. The line containing BC is parallel to the line containing KL l C. ABC ACB D. ABC AKL E. ABC~ AKL F. ABC AKL 13

14 25. The diagram shows MN graphed on a coordinate plane. Point P lies on MN and is ¾ of the way from M to N. What are the coordinates of point P? Enter only your answer. 26. The figure shows line segment JK and a point P that is not collinear with points J and K. Suppose that line segment J K is the image of line segment JK after a dilation with scale factor of 0.5 that is centered a point P. Which statement best describes the position of line segment J K? A. Line segment J K is parallel to line segment JK B. Line segment J K is perpendicular to line segment JK. C. Line segment J K intersects line segment JK at one point, but is not perpendicular to line segment JK. D. Line segment J K lies on the same line as line segment JK. 27. Triangle APQ is the image of ABC under a dilation centered at vertex A with scale factor ½. Triangle RBT is the image of ABC under a dilation centered at vertex B with scale factor ¾. Which statement about ABC, APQ, and RBT is correct? A. All these triangles are similar B. None of the triangles are similar C. Triangles APQ and RBT are not similar because they were dilated using different scale factors. D. Triangles APQ and RBT are not similar because they were dilated with different centers of dilation. 28. A dilation of a center P (0, 0) and a scale factor k is applied to MN. Let M N represent the image of MN after the dilation. Select each correct statement. A. If k > 0, then M N > MN B. If k > 1, then M N > MN C. If 0 < k < 1, then M N < MN D. D. If 0.5 < k < 1.5, then M N < MN E. E. If k =1, then M N = MN F. F. If k = 0.5, then M N 0.5( MN ) 14

15 29. Given the two triangles shown, find the value of x. Select from the drop-down menu to correctly complete the sentence. The value of x is 30. Points X and Z are on a number line, and point Y partitions XY into two parts so that the ratio of the length of XY to the length of YZ is 5:7. The coordinate of X is 1.3, and the coordinate of Y is 3.8. What is the coordinate of Z? Enter your answer in the box. 15