GEOMETRY MIDTERM REVIEW

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1 Name: GEOMETRY MIDTERM REVIEW DATE: Thursday, January 25 th, 2018 at 8:00am ROOM: Please bring in the following: Pens, pencils, compass, ruler & graphing calculator with working batteries (Calhoun will provide a calculator if you do not have one) Highlighters (optional) Midterm Format: 10 Part I multiple choice (2 pts each) 20 total pts. 5 Part II short answer (2 pts each) 10 total pts. 5 Part III short answer (4 pts each) 20 total pts. 2 Part IV short answer (6 pts each) 12 total pts. Total questions: 22 Total points: 62 Page 1

2 1. In the diagram below of, medians AL, BM, and CN intersect at P. If and. a. What is point P called? b. What is the value of x? c. What is the length of PM? d. What is the length of BM? 2. In the diagram below, is shown with extended through point D. If,, and. a. What is the value of x? b. What is m<bcd? c. What is m<bac? d. What is m<abc? e. What is m<acb? Exterior Angle Theorem: Page 2

3 3. Given the diagram below, TG = TR; m S = 2x - 10; m STG = x + 10 m SGT = 6x. Determine the following: A. Find m S. B. Find m TGR. 4. Given the diagram below, TG = TR; If GT =3y + 6 and TR = 5y 8, the determine the following: C. Find TR. D. Find SR. 5. Given: CE AB, which statement is false? 1) AFC BFC 2) AFE BFE 3) AC BC 4) DF FE Page 3

4 6. In the diagram of to the right, given. Prove? 7. Prove: The sum of the angles in a triangle is In the diagram below,,,,, and. Which triangle similarity statement is correct? 1) by AA. 3) by SSS. 2) by SAS. 4) is not similar to. Page 4

5 9. Given: BD bisects ADC and ABC Prove: A C (b) Describe the rigid motion(s) that would map one triangle onto the other. 10. Given: Point P on line AB. Construct: A line through P perpendicular to line AB. [Leave all construction marks.] Page 5

6 11. Given: Circle G Construct an equilateral triangle inscribed in circle shown below. [Leave all construction marks.] 12. Given: Circle G Construct a hexagon inscribed in circle shown below. [Leave all construction marks.] 13. Construct a circumcenter. 14. Construct an incenter. A A B C B C 15. Triangles RST and XYZ are drawn below. If,,,, and, is similar to? Explain your answer. If the triangles are similar, write the similarity statement. Page 6

7 16. Are the triangles shown below similar? Explain. If the triangles are similar, write the similarity statement. 17. To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram. Use the surveyor's information to determine and state the distance from point B to point C, to the nearest yard. 18. In the diagram of below,,,, and.. a. What is the length of BC, to the nearest tenth? b. What is the length of AC, to the nearest tenth? 19. In the diagram below, ABC DEC. If,,, and the perimeter of ABC is 30, what is the perimeter of DEC? Page 7

8 20. In isosceles triangle RST shown below,, M and N are midpoints of and, respectively, and is drawn. If and the perimeter of is 25, determine and state the length of. 21. Triangle ABC is shown in the diagram below. If joins the midpoints of and, which statement is not true? 1) 2) 3) 4) 22. In the diagram of shown below, is drawn from vertex B to point A on, such that.. In,,, and. [Only algebraic solutions can receive full credit.] a) Find m D: Justify your answer using theorems b) Find m BAC : Justify your answer using theorems c) Find m ABC Justify your answer using theorems Page 8

9 23. Given the diagram below, find the unknown angles. Reason(s) 24. Given the diagram below, find the unknown angles. Reason(s) 25. Using a compass and straightedge, construct and label D' E ' F ', the image of DEF after a dilation with a scale factor of 2 and the center of dilation at D. [Leave all construction marks.] 26. Find the center of dilation that maps ABC to ABC and label it O. Page 9

10 27. Write the method that is being illustrated in the following triangles to prove congruency. Then, state if that is a valid method. a) b) c) d) e) 28. On the set of axes below, rectangle ABCD can be proven congruent to rectangle KLMN using which transformation? 1) rotation 2) translation 3) reflection over the x-axis 4) reflection over the y-axis 29. Given: A E, and AE bisects BC at D. Which of the following methods can be used to prove that the triangles are congruent? [1] Side-Angle-Side (SAS) [2] Angle-Side-Angle (ASA) [3] Side-Side-Side (SSS) [4] Angle- Angle Side- (AAS) 30. Given the quadrilaterals shown at the right. Which rigid motion will verify that quadrilateral PART is congruent to quadrilateral HGFE? 31. Which rigid motion(s) will verify that ΔABC is congruent to ΔDFE as shown at the below? Page 10

11 32. Given: TQ is the perpendicular bisector to RS. Prove: R S T R Q S (b) Describe the rigid motion(s) that would map one triangle onto the other. 33. In,,,, and. What is the length of? 34. Page 11

12 35. Given right ΔABC and right ΔDEF marked as shown at the right. ΔFGC is isosceles. Determine which method will prove ΔABC is congruent to ΔDEF? 36. In and,. Which additional information would prove? 1) 3) 2) 4) 37. A flagpole casts a shadow meters long. Tim stands at a distance of meters from the base of the flagpole, such that the end of Tim's shadow meets the end of the flagpole's shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter. 38. In the diagram below,,, and.which statement is true? 1) is obtuse. 2) is isosceles. 3) 4) is scalene. 39. Identify the sequence of basic rigid motions performed the constructions below. Page 12

13 40. Identify the sequence of basic rigid motions performed the constructions below. 41. As graphed on the set of axes below, is the image of after a sequence of transformations. Is congruent to? Use the properties of rigid motion to explain your answer. 42. The grid below shows and. Let be the image of after a rotation about point A. Determine and state the location of B' if the location of point C' is. Explain your answer. Is congruent to? Explain your answer. Page 13

14 43. Triangle XYZ, shown in the diagram below. On the same set of axes provided, graph and label X Y Z, the image of Triangle XYZ after the translation three units right and two units down and then is reflected over the line x= U, V, and W are the midpoints of the sides of XYZ. If UW 4x 1 and, YZ 5x 4 what is the length of UW? Y U V X W Z 45. Triangle ABC has coordinates,, and. a) On the grid below, draw and label. b) Graph and state the coordinates of, the image of after the composition. c) Write a single transformation equivalent to d) Did the composition preserve orientation? Justify your response. e) Is the composition a rigid motion? Justify your response. Page 14

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