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GEO REVIEW TEST #1 Name: 1. 2. Date: In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus (2) trapezoid (4) parallelogram 4. In the accompanying diagram, AB and CD intersect at E, E is the midpoint of AB, and OA = OB. Which statement can be used to prove ^ADE = ^BCE 3. ! In the accompanying diagram, lines AB and ! CD intersect at point E. If mOAED = (x + 10) and mOCEB = 50, nd x. (1) ASA = ASA (3) SSS = SSS (2) HL = HL (4) SAS = SAS 5. The measures of two complementary angles are represented by x + 5 and 4x 15. Find the value of x. 6. If a base angle of an isosceles triangle measures 35, nd the measure of the vertex angle. State the congruence relation for ^ ABC and ^DEF. (1) SSS (2) SSA (3) ASA (4) SAS page 1 7. In the gure, IN = CK and IK k NC. What congruence statement proves ^KNI = ^ NKC ? 9. In the accompanying diagram, parallel lines ! ! ! AB and CD are cut by transversal GH at E and F, respectively. If mOBEF = (3x + 60), nd the value of x. 10. What is the image of point A after a rotation of 90 in the clockwise direction? (1) SSS (2) SAS (3) ASA (4) not necessarily congruent G E D B The drawing shows how to— F H C A 8. (1) B (2) C (3) E (4) F (1) bisect an angle (2) copy an angle (3) create the angles of a parallelogram (4) create the sides of an equilateral triangle 11. What is the rotational symmetry of a regular nonagon? (1) 60 page 2 (2) 45 (3) 40 (4) 30 GEO REVIEW TEST #1 12. Melissa is walking around the outside of a building that is in the shape of a regular polygon. She determines that the measure of one exterior angle of the building is 60 . How many sides does the building have? (1) 6 13. (2) 9 (3) 3 16. In the accompanying diagram, OACD is an exterior angle of ^ABC. If mOB = 40, mOA = 2x, and mOACD = 3x. What is the value of x ? 17. In the accompanying diagram of rhombus ABCD, the lengths of the sides AB and BC are represented by 3x 4 and 2x + 1, respectively. Find the value of x. (4) 12 The drawing shows how to— (1) construct a perpendicular bisector (2) draw complementary angles (3) bisect an angle (4) inscribe an angle 14. 15. If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be (1) obtuse (3) acute (2) right (4) isosceles Find the sum of the measures of the interior angles of a hexagon. page 3 GEO REVIEW TEST #1 18. State the congruence relation for ^XYZ and ^PQR. 20. In the accompanying diagram of parallelogram ABCD, mOA = 2x 10 and mOB = 5x + 15. Find x. 21. The Corresponding Angles Conjecture states that if two parallel lines are cut by a transversal, the alternate interior angles are congruent. The picture below shows this relationship. (1) ASA (2) AAA (3) SAS (4) not necessarily congruent 19. The Corresponding Angles Conjecture states that if two parallel lines are cut by a transversal, the corresponding angles are congruent. The picture below shows this relationship. To test this conjecture, which pair of congruent angles are alternate interior angles? Which of these congruent angles are corresponding angles? (1) O1 and O4 (3) O4 and O8 (2) O1 and O3 (4) O4 and O3 page 4 (1) O1 and O4 (3) O4 and O8 (2) O2 and O8 (4) O3 and O5 GEO REVIEW TEST #1 22. 23. ! In the accompanying diagram, ABC is a ! ! straight line, BD ? BE, and mOCBE = 50. Find mOABD. 25. Which quadrilateral does not always have congruent diagonals? In the diagram, ^P0 Q0 R0 is the image of ^ PQR. Which type of transformation is shown? (1) re ection (3) translation (2) rotation (4) dilation (1) isosceles trapezoid (2) rectangle (3) rhombus (4) square 26. In the accompanying diagram, parallel lines ` and m are cut by transversal t. Which statement about angles 1 and 2 must be true? 24. In parallelogram ABCD shown below, diagonals AC and BD intersect at E. (1) O1 = O2 (2) O1 is a complement to O2 (3) O1 is a supplement to O2 Which statement must be true? (1) AC = DB (3) ^AED = ^ CEB (2) OABD = OCBD (4) ^DCE = ^BCE (4) O1 and O2 are right angles page 5 GEO REVIEW TEST #1 27. What is the sum, in degrees, of the measures of the interior angles of a stop sign, which is in the shape of an octagon? (1) 360 28. (2) 1,080 (3) 1,440 31. (4) 1,880 ! In the accompanying diagram, AB is ! ! ! parallel to CD, and AB and CD are cut ! by transversal EF at points G and H, respectively. If mO EGA = (2x + 30) and mOEHC = (x + 80), nd x. 32. 29. ! In the accompanying diagram, lines AB, ! ! CD, and EF intersect at G. If mODGB = 35 and mOCGF = 75, nd mOAGE. A translation maps J(1; 4) onto K(7; 3). Find the coordinates of the image of L(5; 10) under the same translation. 33. 30. In parallelogram ABCD, the measure of O ABC is 130 . Find the measure, in degrees, of ODAB. (1) (11; 3) (3) (1; 17) (2) ( 11; 7) (4) ( 1; 17) ! ! In the accompanying diagram, AB k CD, ! ! EF intersects AB at E and CD at F, and ! GH intersects AB at G and EF at H. If mOEGH = 40, mOGHE = 80, and mOEFD = x, what is the value of x ? Two angles are supplementary. If one angle measures twice the other, nd the number of degrees in the smaller angle. page 6 GEO REVIEW TEST #1 34. A quadrilateral with exactly one pair of parallel sides is a 38. Which geometric symmetry? gure has 72 rotational (1) rhombus (3) square (1) square (2) rectangle (4) trapezoid (2) regular pentagon (3) rhombus (4) regular hexagon 35. 36. A translation moves A( 3; 2) to A0 (0; 0). Find B0 , the image of B(5; 4), under the same translation. (1) (8; 2) (3) (7; 3) (2) (2; 6) (4) ( 8; 2) 39. What is mOACB? In ^ABC, mO A = 95, mO B = 50, and mOC = 35. Which expression correctly relates the lengths of the sides of this triangle? (1) AB < BC < CA (3) AC < BC < AB (2) AB < AC < BC (4) BC < AC < AB (1) 40 40. 37. What is the rotational symmetry of an equilateral triangle? (1) 120 (2) 100 (3) 90 ! ! In the accompanying diagram, AB k CD, mOCAB = 80, and mODCB = 40. (2) 60 (3) 80 (4) 120 What is the measure, in degrees, of each exterior angle of a regular hexagon? (1) 45 (2) 60 (3) 120 (4) 135 (4) 60 page 7 GEO REVIEW TEST #1 Problem-Attic format version 4.4.274 c 2011–2016 EducAide Software _ Licensed for use by Margaret Ferry Terms of Use at www.problem-attic.com GEO REVIEW TEST #1 1. Answer: 1 2. Answer: 1 3. Answer: Objective: 4. Answer: 5. Answer: 6. Answer: 7. Answer: Objective: 1 G.CO.7 40 20 110 2 G.CO.7 11/04/2016 18. Answer: Objective: 4 G.CO.7 19. Answer: Objective: 3 G.CO.9 20. Answer: 25 21. Answer: Objective: 4 G.CO.9 22. Answer: 40 23. Answer: 3 24. Answer: 3 8. Answer: Objective: 2 G.CO.12 9. Answer: 25. Answer: Objective: 2 G.CO.5 20 26. Answer: 3 27. Answer: 2 28. Answer: 50 29. Answer: Objective: 1 G.CO.6 30. Answer: 60 31. Answer: 50 32. Answer: 70 33. Answer: 60 34. Answer: 4 10. Answer: Objective: 4 G.CO.2 11. Answer: Objective: 3 G.CO.3 12. Answer: 1 13. Answer: Objective: 3 G.CO.12 14. Answer: 1 15. Answer: 720 16. Answer: 40 17. Answer: 5 Teacher's Key 35. Answer: Objective: 1 G.CO.6 36. Answer: 2 37. Answer: Objective: 1 G.CO.3 38. Answer: Objective: 2 G.CO.3 39. Answer: 2 40. Answer: 2 Page 2