Mrs. DosSantos. Common Core Geometry Regents Review

Transcription

1 Mrs. DosSantos Common Core Geometry Regents Review June 4, 2018

2 Name: CC Geometry Regents Review 1) Find the perimeter in simplest radical form for a triangle with side lengths of 5 18, 20, and 32 2) A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container? 3) The image of DABC under a translation is D A'B'C'. Under this translation, B (3, -2) maps onto B (1, -1). Using this translation, the coordinates of image A are (-2,2). Determine and state the coordinates of point A. 4) The base of a pyramid is a rectangle with a width of 6cm and a length of 8cm. Find, in centimeters, the height of the pyramid if the volume is 288 cm 3.

3 5) In the diagram below, QM is a median of triangle PQR and point C is the centroid of triangle PQR. If QC = 5x and CM = x + 12, determine and state the length of QM. 6) Which geometric principle is used in the construction shown below? 1) The intersection of the angle bisectors of a triangle is the center of the inscribed circle. 2) The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. 3) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle. 4) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.

4 8) 7) Find x.

5 9) As shown in the diagram below, is a diagonal of trapezoid STAR,, m ATS = 48, m RSA = 47, and m ARS = 68. Determine and state the longest side of ΔSAT AND Justify your response. Longest side: Justification: 10) Directed line segment NC has coordinates of N (-2, -3) to C(8, 2). Find and state the coordinates of point Y such that NY :YC is in the ratio 2:3. 11) The line y = - 12x - 9 is dilated by a scale factor of 2 and centered at the origin. What is 3 the equation of the image of the line after the dilation?

6 12) Given: Quadrilateral QRST RS ST SR QR ST QT. Prove: < RQS <TQS

7 13) The vertices of a triangle are E(6, -3), D(-5, -3), C(6, -1). What is the coordinate of its centroid? 14) What is the perimeter of a rhombus whose diagonals are 24 and 10? 15) The volume of a sphere is approximately cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter? 16) The measures of angles M and T of a parallelogram MINT are in the ratio of 5:7. Find the measure of the obtuse angle. 17) Write an equation represents circle O with center and radius 9?

8 Mrs. DosSantos Common Core Geometry Regents Review June 11, 2018

9 Name: CC Geometry Regents Review 1) Segment AB is the diameter of circle M. The coordinates of A are ( 4,3). The coordinates of M are (1,5). What are the coordinates of B? 2) In the accompanying diagram of ABC, AC is extended to D, DEF, BEC, AFB, m B = 50, m BEF = 25, and m ACB = 65. What is m D? 3) Given the isosceles triangle below, Find the values of x & y.

10 4) Write an equation of the perpendicular bisector of the line segment whose endpoints are (-5, 5) and (9, 7). [The use of the grid is optional.] 5) The line y = - 12x - 9 is dilated by a scale factor of 2 and centered at the origin. What is 3 the equation of the image of the line after the dilation? 6) Peter says that these triangles are similar. J.C. says that they are not similar. Identify whether they are similar or not and justify your response with geometric theorems. Diagram not drawn to scale.

11 7) Suppose we apply dilation by a factor of 2. 4, centered at the origin of the Cartesian system, to the segment AB in the figure below. The coordinates of point A are (0, 4) and the coordinates of point B are (3,0). State the coordinate of the images A' and B' of the points A and B under this dilation and calculate the distance d = A'B'. A B Calculations: A B = 8) Find the value of WY. 9) Solve for x.

12 SOLVE FOR X. 10) 11) 12) Determine whether the triangles below are similar. Justify your answer. Show all work. 13) The measures of two sides of a triangle are 9 and 15, between what two numbers must the third side fall? Write an inequality to represent your answer.

13 14) Write a composition of transformations. Identify if either of these compositions above are glide reflections? 15) Using coordinate geometry, determine the specific quadrilateral type for BEAR. Given: Quadrilateral BEAR B (3,2) E(4,11) A(11,13) R(10,4) You must show proof of calculations and explain your reasoning.

14 16) Using the diagram below, answer questions a-c. B A C D a) Solve for x. b) Identify, using angles and sides, the type of triangle it is. c) The longest side is. 17) Which ratio represents cos B in the accompanying diagram of ABC? ) Sonar on a destroyer detects a submarine at a depth of 200 m. If the angle is 31 o. Find, to the nearest meter, the distance between the two vessels.

15 19) You are a block away from a skyscraper that is 780 ft. tall. Your friend is between the skyscraper and yourself. The angle of elevation from your position to the top of the skyscraper is 42 o. The angle of elevation from your friend s position to the top of the skyscraper is 71 o. To the nearest foot, how far are you from your friend? 20) Five cubes of ice with an edge 3 cm each are left to melt in a right cylinder shaped glass with a height of 16 cm and a radius of 5 cm. How high will the water rise when they have melted? Round your answer to the nearest tenth of a cm. 21) The slope of QR = x -1 4 and the slope of ST = 8 3. If QR ^ ST, determine and state the value of x.

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