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Name_________________________________ PARCC Review 1. Select the drop-down menus to correctly complete each sentence. 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 E. ray 1 Μ Μ Μ Μ one is one of those 4. Using a compass and a straightedge, a student constructed a triangle in which ππ sides. The compass is opened to a set length and two intersecting arcs are drawn above Μ Μ Μ Μ ππ 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 βπππ is 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 Part B Select the correct phrase to complete the sentence If the opening of the compass is then βπππ will be equilateral 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 length less Μ Μ Μ Μ . Jerichoβs markings are useful for the construction of which of than the length of segment ππ the figures listed? Select all that apply A. a 60° angle B. Μ Μ Μ Μ a bisector of ππ C. line perpendicular to Μ Μ Μ Μ ππ D. a rhombus with Μ Μ Μ Μ ππ as one diagonal E. an equilateral triangle with side Μ Μ Μ Μ ππ Part B The first steps of Jerichoβs secondβs construction are shown. After drawing arcs from point π and point π , he adjusted the compass length using the intersection of the arc from point π with Μ Μ Μ Μ βββββ . Which figure is he constructing? ππ and ππ Μ Μ Μ Μ Μ through point R A. the bisector of ππ B. an angle congruent toβ π ππ with vertex R Μ Μ Μ Μ Μ C. a line through point R that is parallel to ππ D. a circle containing points P, Q ,and R 3 6. Quadrilateral ABCD is shown graphed in the π₯π¦- coordinate plane. Part A Quadrilateral ABCD will be translated according to the rule (π₯, π¦) β (π₯ + 3, π¦ β 4) to form AβBβCβDβ. Select the correct orientation of AβBβCβDβ and place it correctly on the plane. Part B Quadrilateral ABCD maps onto AβBβCβDβ. It will undergo a different transformation that will map π΄(β6,3) to Aβ, B(-4,5) to Bβ, C (-1,6) to Cβ , and D (-3,2) to Dβ .The transformation will consist of a reflection over the y-axis followed by a translation. Point Dβ is shown plotted in the plane after the transformation. Plot the point Aβ in the plane. 4 7. Part A Line π passes through the points (β4, β7) and (2, β3) on the coordinate plane. Line π passes through the points (β4, 1) and (2, π€). For what value of w is line m parallel to line π? Enter your answer in the box. Part B Given the figure, write the expression that can replace π‘ and will guarantee that lines π and π are parallel. Support your answer. 5 8. The diagram shows regular hexagon ABCDEF with center at O. Justine made these claims. ο· The only lines of symmetry for regular hexagon ABCDEF are the lines that contain one vertex and O. ο· 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 JβKβLβ in the π₯π¦- coordinate plane. Which transformations will result in βπ½πΎπΏ β βπ½β² πΎ β² πΏβ² ? A. (π₯ , π¦) ο (βπ₯, βπ¦) B. (π₯, π¦) ο (βπ₯ , π¦) C. (π₯, π¦) ο (π₯, π¦ β 5) D. (π₯, π¦) ο (π₯ + 3, π¦ β 5) E. (π₯, π¦)ο (2π₯, 3π¦) F. (π₯, π¦) ο (βπ₯, π¦ + 3) 6 10. In the figure, π Η π. Transversals π‘ and π€ intersect at point πΏ. Part A What is the missing reason in step 3? A. Alternate interior angles along parallel lines are congruent. B. Alternate exterior angles along parallel lines are congruent. C. Corresponding angles along parallel lines are congruent D. Vertical angles are congruent Part B Consider the proof of π β π given that β πΏπ»πΎ ~ β πΏπ½π. If β πΏπ»πΎ ~ β πΏπ½π, then β πΏπ»πΎ β β πΏπ½π because corresponding angles in similar triangles are congruent. Which statement concludes the proof? A. If β πΏπ»πΎ β β πΏπ½π then π β π because when base angles are congruent, the lines are parallel. B. If β πΏπ»πΎ β β πΏπ½π then π β π because when corresponding angles are congruent, the lines are parallel C. If β πΏπ»πΎ β β πΏπΎπ» then π β π because when alternate exterior angles are congruent, the lines are parallel D. If β π½πΏπ β β π»πΏπΎ, then π β π because when corresponding angles are congruent the lines are parallel 7 11. Triangle π΄π΅πΆ is shown in the π₯π¦- coordinate plane. The triangle will be translated 2 units down and 3 units right to create triangle π΄βπ΅βπΆβ. Indicate whether each of the listed parts of the image will or will not be the same as the corresponding part in which the preimage (triangle π¨π©πͺ) by selecting the appropriate box in the table. 8 12. The right triangle in the coordinate plane is rotated 270° clockwise about the point (2, 1) and then reflected across the π¦ βaxis to form triangle AβBβC. Draw in the appropriate orientation for triangle AβBβC into the correct position on the coordinate plane (sketch it). 9 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 AβBβCβ. What are the coordinates of Cβ after the reflection? A. (-6, 4) B. (3, -2) C. (4, -6) D. (6, -4) Part B Triangle ABC in the xy- coordinate plane will be rotated 90 degrees counterclockwise about point A to form triangle AβBβCβ. Which graph represents AβBβCβ? 10 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? A. Through any two points, there is exactly one line B. Though a point not on a line, there is exactly one line parallel to the given line C. If two lines cut by a transversal form congruent corresponding angle, then the lines are parallel. D. If two lines cut by a transversal form congruent alternate interior angles, then the lines are parallel. Part B Which pairs of angles congruence or equalities should be used for the statement in step 2? Indicate all such pairs. 11 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 15. Octagon PQRSTVWZ is a regular octagon with its center at point C. Which transformations will map octagon PQRSTVWZ onto itself? Select each correct transformation Μ Μ Μ Μ A. reflecting over ππ Μ Μ Μ Μ Μ B. reflecting over π π Μ Μ Μ Μ C. reflecting over ππ D. rotating 45° clockwise around point Z. E. rotating 135° clockwise around point C F. rotating 90° counterclockwise around point C. 12 16. Part A βABC meets the given criteria ο· The perimeter of triangle ABC is 50 units, ο· Only two of the sides have the same length ο· The third side is 16 units long, given in the diagram What are the coordinates of point C that will meet the criteria for triangle ABC? A. ( 6.25,8 ) B. ( 8, 6.25 ) C. ( 8, 15 ) D. ( 15, 8 ) Part B 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 βπ΄π΅πΆ? Provide valid mathematical reasoning and calculations to support your answer. Enter your answer, your reasoning, and your calculations in the space provided 13 17. Given: In βπ΄π΅πΆ shown, Μ Μ Μ Μ π΅π΄ β Μ Μ Μ Μ π΅πΆ Part A Select from the drop down menus to correctly complete step 2 of the proof. Part B 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 congruen 14 18. In the diagram, quadrilaterals πΉπ΅π΄πΊ and πΆπ·πΈπΉ are rectangles How long is Μ Μ Μ Μ π·πΈ rounded to the nearest tenth? Enter your answer in the box. 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. 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 point on the number line to plot the point. 15 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 π passes through point C and has a slope of -2. Enter your answers in the boxes: A dilation of line π with center π΄ and a scale factor of 3 will produce a new line through point Cβ, the image of point C with coordinates ( slope of , ) and with a . Hint β create a line segment and dilate it. (1,0) is another point on line π. Create another triangle from on the point of dilation. 16 23. Triangle π is dilated from center A by a scale factor of 2 to form triangle Q. The vertici\es 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 place on the coordinate plane to plot the point. 17 24. βπ΄π΅πΆ is dilated from the center π΄ by a factor not equal to 1 to form βπ΄πΎπΏ. Which of the statements must be true? Select all that apply. A. Μ Μ Μ Μ π΄π΅ and Μ Μ Μ Μ π΄πΎ lie on the same line. B. The line containing Μ Μ Μ Μ π΅πΆ is parallel to the line containing Μ Μ Μ Μ πΎπΏ . C. β π΄π΅πΆ β β π΄πΆπ΅ D. β π΄π΅πΆ β β π΄πΎπΏ E. βπ΄π΅πΆ~βπ΄πΎπΏ F. βπ΄π΅πΆ β βπ΄πΎπΏ Μ Μ Μ Μ Μ Μ graphed on a coordinate plane. 25. The diagram shows ππ Point P lies on Μ Μ Μ Μ Μ Μ ππ and is ¾ of the way from M to N. What are the coordinates of point P? 26. The figure shows line segment JK and a point P that is not collinear with points J and K. Suppose that line segment JβKβ 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 JβKβ? A. Line segment JβKβ is parallel to line segment JK B. Line segment JβKβ is perpendicular to line segment JK. C. Line segment JβKβ intersects line segment JK at one point, but is not perpendicular to line segment JK. D. Line segment JβKβ lies on the same line as line segment JK. 18 27. Triangle π΄ππ is the image of βπ΄π΅πΆ under a dilation centered at vertex A with scale factor ½. Triangle π π΅π is the image of βπ΄π΅πΆ under a dilation centered at vertex B with scale factor ¾. Which statement about βπ΄π΅πΆ, βπ΄ππ, andβ π π΅π 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 π is applied to Μ Μ Μ Μ Μ ππ. Let Μ Μ Μ Μ Μ Μ πβπβ represent the image of Μ Μ Μ Μ Μ ππ after the dilation. Select each correct statement. A. If π > 0, then πβπβ > ππ B. If π > 1, then πβπβ > ππ C. If 0 < π < 1, then πβπβ < ππ D. If 0.5 < π < 1.5, then πβπβ < ππ E. If π = 1, then πβπβ = ππ F. If π = 0.5, then πβπβ = 0.5( ππ ) 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 19 30. Points X and Z are on a number line, and point Y partitions Μ Μ Μ Μ ππ into two parts so that the ratio of the length of Μ Μ Μ Μ ππ to the length of Μ Μ Μ Μ ππ is 5:7. The coordinate of X is 1.3 and the coordinate of Y is 3.8. What is the coordinate of Z? 20