Name: Period: Date: Geometry Midyear Exam Review. 3. Solve for x. 4. Which of the following represent a line that intersects the line 2y + 3 = 5x?

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1 Name: Period: Date: Geometry Midyear Exam Review 1. Triangle ABC has vertices A(-2, 2), B(0, 6), and C(7, 5). a) If BD is an altitude, find its length. b) XY is the midsegment parallel to AC. Find the coordinates of X and Y. 2. Triangle DEF has vertices D(2, -4), E(5, 0), and F(- 2, 2). Put the angles D, E, and F in order from smallest to largest. 3. Solve for x. 4. Which of the following represent a line that intersects the line 2y + 3 = 5x? A. y = 5 7 x B. 5x 2y = 6 C. y 1 = 5 (x + 4) 2 D. y = 3 2 x Which of the following represents a line perpendicular to y = 2x + 7? I. y = 2x - 7 II. y = 1 x III. y + 5 = 1 (x + 3) 2 A. I only B. II only C. II and III D. None of the above 7. Point P divides AB so that AP. If point A lies PB = 1 4 at (2, 7) and P lies at (4, 6), find the coordinates of Point B. A. (2.4, 6.8) B. (12, 2) C. (12, 12) D. (3.6, 6.2) 9. Use the properties of the diagonals and the definition of a rhombus to solve for variables m and n. 6. Point P partitions directed segment AB in the ratio of 3:4. If A is at (-9,-9) and B is (5,-2), find the coordinates of P. A. (-3, -7) B. (-3, -6) C. (-6, -6) D. (-4, -6) 8. a. Draw a rhombus and name it ABCD. Why is your figure a rhombus? b. Draw diagonals AC and BD. What properties do the diagonals of a rhombus have? c. If two consecutive sides in a parallelogram are congruent, is the parallelogram a rhombus? 10. Solve for x. 11. Solve for m f. 12. Solve for m i. 13. Which triangle congruence postulate(s) or theorem(s) could be used to prove ABC DEC? a) SAS b) HL c) SSS d) SSA e) These triangles cannot be proven congruent with the given information.

2 14. C is the midpoint of AD; CBE CEB. Which triangle congruence postulate(s) or theorem(s) could be used to prove ACB DCE? I. SSS II. SSA III. AAS IV. HL 15. Given CAB = DBA = 90 o ; AC BD ; AE BE a) Which triangle congruence postulate(s) or theorem(s) could be used to prove CAB DBA? b) Which triangle congruence postulates or theorem(s) could be used to prove CEA DEB? 1. III only b) IV only c) I and IV d) II and III 16. Which would not be sufficient to prove the triangles congruent? a) B E b) A D c) CA BA ;FD DE d) AC = DF 17. Which point is the circumcenter of ABC? Justify your reasoning. 18. Construct the incenter of LPQ. 19. Given: ARG, median RL, centroid E, and altitude RB. If BL = 7, RB = 24, find EL. 20. Construct the median from F to side AQ.

3 21. For an obtuse triangle, which points of concurrency are located outside the triangle? Questions 22 and 23 refer to IBR. 22. Which of the following is a true statement? Select all that apply. a. The length o IB is twice that of NV. b. BO = OI c. RV = RN d. NV and BI are parallel e. BN = NR 24. In the diagram below, D is the midpoint of CE, B is the midpoint of AC, and F is the midpoint of AE. Let AE = x 2 3x 14 and BD = 2x Find AE and BD. 23. Which of the following is a true statement? Select all that apply a. The length of BR is twice that of OV b. BO = BN c. RV = RN d. BR and OV are parallel e. NV and ON are parallel 25. Find the measure of each exterior angle of a. a regular hexagon. b. A regular 17-gon 26. Give an expression for the difference between the measure of an exterior angle and the measure of an interior angle of a regular n- gon. 27. Given a point on a line, construct the perpendicular to the line at the given point P. 28. Construct the line that is perpendicular to AB and that passes through point P. 29. Construct the altitude from B to AC for ABC. Construct the altitude from vertex A to BC for ABC. 30. Which point of concurrency is equidistant from: a) the three sides of a triangle? b) the three vertices of a triangle? c) creates 6 triangles with equal area? 31. Which point of concurrency is a) the intersection of the medians of the triangle? b) the intersection of the altitudes of the triangle? c) the intersection of the perpendicular bisectors of the triangle?

4 32. Always/ Sometimes/ Never a) The centroid is in the triangle. b) The circumcenter is in the triangle. c) The incenter is outside of the triangle. d) The orthocenter is on the triangle. d) is the intersection of the angle bisectors of the triangle? e) the center of a circumscribed circle? f) the center of an inscribed circle? 33. AU, BV, and CW are the medians of ABC. For the following, show work algebraically. a) If AP = x2 and PU = 6x, find all possible value(s) of x. b) If BP = w2 32 and PV = w 4, find all possible value(s) of w, BP, and PV. c) If CW = 2k2 5k 12 and CP = k2 15, find all possible value(s) of k and PW. 34. Find the perimeter of WSTV

5 43. ABCD is a parallelogram. Which of the following conclusions, if any, is/are necessarily true? (There may be more than one!) Suppose XY bisects ZXW. Find all possible values of m ZXW if m ZXW = 12x + 14 and m YXW = x 2.