GEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?


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1 GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10) and m CEB = 50, find x. (2) trapezoid (4) parallelogram 2. In the accompanying diagram, AB and CD intersect at E, E is the midpoint of AB, and A = B. Which statement can be used to prove ADE = BCE (1) ASA = ASA (3) SSS = SSS 5. The measures of two complementary angles are represented by x + 5 and 4x 15. Find the value of x. (2) HL = HL (4) SAS = SAS 3. State the congruence relation for ABC and DEF. (1) SSS (2) SSA 6. If a base angle of an isosceles triangle measures 35, find the measure of the vertex angle. (3) ASA (4) SAS page 1
2 7. In the figure, IN = CK and IK 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 m BEF = (3x + 60), find the value of x. (1) SSS (2) SAS (3) ASA (4) not necessarily congruent 10. What is the image of point A after a rotation of 90 in the clockwise direction? 8. The drawing shows how to D G E B F C A H (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 (2) 45 (3) 40 (4) 30 page 2 GEO REVIEW TEST #1
3 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? 16. In the accompanying diagram, ACD is an exterior angle of ABC. If m B = 40, m A = 2x, and m ACD = 3x. What is the value of x? (1) 6 (2) 9 (3) 3 (4) The drawing shows how to (1) construct a perpendicular bisector (2) draw complementary angles (3) bisect an angle (4) inscribe an angle 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. 14. If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be (1) obtuse (2) right (3) acute (4) isosceles 15. Find the sum of the measures of the interior angles of a hexagon. page 3 GEO REVIEW TEST #1
4 18. State the congruence relation for XYZ and PQR. 20. In the accompanying diagram of parallelogram ABCD, m A = 2x 10 and m B = 5x Find x. (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. 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. Which of these congruent angles are corresponding angles? To test this conjecture, which pair of congruent angles are alternate interior angles? (1) 1 and 4 (3) 4 and 8 (1) 1 and 4 (3) 4 and 8 (2) 2 and 8 (4) 3 and 5 (2) 1 and 3 (4) 4 and 3 page 4 GEO REVIEW TEST #1
5 22. In the accompanying diagram, ABC is a straight line, BD BE, and m CBE = 50. Find m ABD. 25. In the diagram, P Q R is the image of PQR. Which type of transformation is shown? 23. Which quadrilateral does not always have congruent diagonals? (1) isosceles trapezoid (2) rectangle (3) rhombus (4) square (1) reflection (2) rotation (3) translation (4) dilation 26. In the accompanying diagram, parallel lines l 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) 1 = 2 (2) 1 is a complement to 2 Which statement must be true? (3) 1 is a supplement to 2 (1) AC = DB (3) AED = CEB (4) 1 and 2 are right angles (2) ABD = CBD (4) DCE = BCE page 5 GEO REVIEW TEST #1
6 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? 31. In parallelogram ABCD, the measure of ABC is 130. Find the measure, in degrees, of DAB. (1) 360 (2) 1,080 (3) 1,440 (4) 1, 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 m EGA = (2x + 30) and m EHC = (x + 80), find x. 32. In the accompanying diagram, lines AB, CD, and EF intersect at G. If m DGB = 35 and m CGF = 75, find m AGE. 29. A translation maps J(1, 4) onto K(7, 3). Find the coordinates of the image of L(5, 10) under the same translation. (1) (11, 3) (2) ( 11, 7) (3) (1, 17) (4) ( 1, 17) 33. In the accompanying diagram, AB CD, EF intersects AB at E and CD at F, and GH intersects AB at G and EF at H. If m EGH = 40, m GHE = 80, and m EFD = x, what is the value of x? 30. Two angles are supplementary. If one angle measures twice the other, find the number of degrees in the smaller angle. page 6 GEO REVIEW TEST #1
7 34. A quadrilateral with exactly one pair of parallel sides is a 38. Which geometric figure has 72 rotational symmetry? (1) rhombus (2) rectangle (3) square (4) trapezoid (1) square (2) regular pentagon (3) rhombus (4) regular hexagon 35. A translation moves A( 3, 2) to A (0, 0). Find B, the image of B(5, 4), under the same translation. (1) (8, 2) (2) (2, 6) (3) (7, 3) (4) ( 8, 2) 39. In the accompanying diagram, AB CD, m CAB = 80, and m DCB = In ABC, m A = 95, m B = 50, and m C = 35. Which expression correctly relates the lengths of the sides of this triangle? What is m ACB? (1) 40 (2) 60 (3) 80 (4) 120 (1) AB < BC < CA (2) AB < AC < BC (3) AC < BC < AB (4) BC < AC < AB 37. What is the rotational symmetry of an equilateral triangle? 40. What is the measure, in degrees, of each exterior angle of a regular hexagon? (1) 45 (2) 60 (3) 120 (4) 135 (1) 120 (2) 100 (3) 90 (4) 60 page 7 GEO REVIEW TEST #1
8 ProblemAttic format version c EducAide Software Licensed for use by Margaret Ferry Terms of Use at GEO REVIEW TEST #1 11/04/ Objective: G.CO.7 4. Answer: Objective: G.CO.7 8. Objective: G.CO Answer: 4 Objective: G.CO Objective: G.CO Objective: G.CO Answer: Answer: Answer: Answer: 4 Objective: G.CO Objective: G.CO Answer: 4 Objective: G.CO Answer: Objective: G.CO Answer: Objective: G.CO Answer: Answer: Answer: Answer: Answer: 4
9 Teacher s Key Page Objective: G.CO Objective: G.CO Objective: G.CO
2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
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