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Midterm Review Name: Date: li83qzk8 Draw pictures and show work as appropriate. 1. 3. Which shape, if rotated 90 , will coincide with itself? (“Coincide” means means there's an exact match between the set of points, or one shape will lay perfectly on top of the other.) A. rectangle B. equilateral triangle C. parallelogram D. square Look at this gure: If the gure is rotated a certain number of degrees, the transformed gure will coincide with (overlap) the original. Which of these cannot be the rotation? A. C. 2. 240 180 B. 120 D. 320 What is the the rotational symmetry of a rhombus? 4. A. 120 B. 100 C. 90 D. 60 Which of the following letters does not exhibit line symmetry? A. page 1 X B. Y C. W D. Z 5. Given a ^ABC in a coordinate plane and its image gure ^A0 B 0 C 0 after any translation, which of the following are always true? I. 8. The distance AA0 and BB 0 are equal. AA0 and III. The distances equal. BC 0 II. The lines BB 0 and are parallel. B0C are IV. mOA = mOA0 6. A. I only B. IV only C. I and II only D. I, II and IV In the gure, mOCNA = mOWAN and CN = WA. What congruence statement proves ^CAN = ^WNA ? A. SAS B. ASA C. SSA D. not necessarily congruent ^DEF is labeled in a clockwise direction. After a sequence of translations, R is the translation of ^ DEF . a) After 3 translations, what is the orientation of R? 9. b) When is the orientation of R not the same as ^DEF ? 7. State the congruence relation for ^FLE and ^FUE. A. ASA B. AAA C. SSA D. SSS page 2 In the diagram, AC = AD and AB bisects OA. Which congruence method is therefore used to conclude that ^ABC = ^ADB ? A. ASA B. SSA C. SAS D. AAA Midterm Review 10. If the triangles can be proved congruent using only the information marked on the diagram, what is the reason? A. SSA B. ASA C. SAS D. cannot be proven congruent 11. page 3 In the gure, XYWZ is an isosceles trapezoid. Which pair of triangles can be proved to be congruent with the result that OXWZ = OYZW by CPCTC? A. ^ZPW and ^YPX B. ^XZY and ^YWX C. ^XZW and ^YWZ D. ^XZP and ^YWP Midterm Review 12. Which diagrams show two triangles which must be congruent? I. A. 13. II. II only B. III. I and II only C. If the vertical brace is a line segment of symmetry for the kite, how many pairs of congruent triangles are formed by the 2 braces? A. 5 pairs B. 3 pairs C. 2 pairs D. 1 pair 14. page 4 I and III only D. II and III only The SAS congruency axiom states that two triangles are congruent if: A. two angles and the contained side of one triangle are equal to two angles and the contained angle of the other triangle. B. two sides and the contained angle of one triangle are equal to two sides and the contained angle of the other triangle. C. two angles and a side of one triangle are equal to two angles and a side of the other triangle. D. two sides and the excluded angle of one triangle are equal to two sides and the excluded angle of the other triangle. Midterm Review 15. Which congruency theorem is described below? 17. “In two triangles, if three pairs of sides are equal in length, then the triangles are congruent.” A. 16. SSS B. SAS C. ASA D. In the diagram, lines a, b, and c are parallel, with the two remaining lines intersecting line b at the same point. x, y, and z are measures of angles. To show that y z = x, which of these angle de nitions or relationships is necessary? AAA A. right angles B. acute angles C. obtuse angles D. vertical angles By the ASA congruency axiom, two triangles are congruent when 2 angles and the contained side of one triangle equal of the other triangle. A. at least 2 angles B. any 2 angles and any side C. 2 angles and the contained side D. 3 sides page 5 Midterm Review 18. Given: O1 and O2 are supplementary Prove: mkn Statement Reason 1. O1 and O2 are suppl. Given 2. mO1 + mO2 = 180 def'n of suppl. angles 3. mO3 + mO2 = 180 def'n of straight angles 4. mO1 subtr. property of equality mO3 = 0 5. mO1 = mO3 add. property of equality 6. m k n In the proof, what is the reason for statement 6? A. If two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines are parallel. B. If two lines are cut by a transversal, and the same-side interior angles are congruent, then the lines are parallel. C. If two lines are cut by a transversal, and the alternate exterior angles are congruent, then the lines are parallel. D. If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are parallel. page 6 Midterm Review 19. Given: AD = DC mOBAC = mOBCA Prove: BD bisects OABC statement reason mOBAC = mO BCA (1) AB = BC (2) AD = DC (3) BD = BD (4) ^ABD = ^CBD mO1 = mO 2 (5) (6) In the above proof, what is reason (2)? A. given B. sides opposite equal angles are equal C. isosceles ^ D. CPCTC page 7 Midterm Review 20. Using the given diagram, Rochelle writes a proof to show that if OSEM = OILM, then ^MEL is isosceles. Statement Reason 1. OSEM = OILM 2. OSEM and OMEL are a linear pair OILM and OMLE are a linear pair 1. Given 2. De nition of Linear Pair 3. OSEM and OMEL are supplementary OILM and OMLE are supplementary 3. Linear Pair Postulate 4. OMEL = OMLE 4. 5. ME = EL 5. If two angles of a triangle are =, then the sides opposite them are = 6. ^ MEL is isosceles. 6. De nition of Isosceles Triangle What reason should Rochelle use to justify the fourth step? A. Supplementary angles are congruent. B. Linear pair angles are congruent. C. Angles that are supplements of congruent angles must be congruent. D. Exterior angles are congruent. page 8 Midterm Review 21. 22. Quadrilateral PARK is a parallelogram with OPAK complementary to OKAR. Pentagon ZEBRA is a regular pentagon. Which of the following statements is most useful in proving ^SAR is an isosceles triangle? Which of the following statements is true? I. A. All sides of ZEBRA are equal in length by de nition of regular pentagon. B. mO1 = mO2 = 72 ; by de nition of regular pentagon. C. mO1 + mO3 = 180 ; by de nition of supplementary O's on a line. D. Quadrilateral PARK is a rhombus II. Quadrilateral PARK is a square III. Quadrilateral PARK is a rectangle A. I B. II C. III D. II and III mO3 = mO4; supplements of congruent O's are congruent. 23. Can an right triangle and a equilateral triangle be congruent? Explain your answer. 24. In quadrilateral ABCD, AD = BC, and AB = DC. Which of the following statement(s) are true? I. both pairs of opposite angles are congruent II. both diagonal bisects each other III. the diagonals are equal page 9 A. II only B. III only C. I and II D. II and III Midterm Review 25. ABCD is a parallelogram. E is the midpoint of AD and F is the midpoint of BC. Prove that DEBF is a parallelogram. 27. The drawing shows how to A. B. 26. . draw the sides of a right triangle nd the center of a triangle C. construct an angle with measure 60 D. construct an angle with measure 45 The diagram shows a method for constructing . 28. The two segments formed as a result of a . bisector will always be A. the median of a triangle A. proportional B. congruent B. an angle bisector C. parallel D. perpendicular C. the altitude of a triangle D. the base of an isosceles triangle page 10 Midterm Review 29. Which of the following shows the construction of a perpendicular from a point to a line? 30. A. Which of the following gures shows the construction of an angle bisector? A. B. B. C. C. D. D. page 11 Midterm Review 31. Besides the information implied by the ! ! ! ! diagram, it is true that BE k CF , and CF ? DF . How many distinct pairs of parallel lines are given or implied by the diagram and the sentence? A. 32. B. 2 C. 3 D. Given the information in the diagram, do the triangles have to be similar? 4 A. Yes. The right triangle is 3 times the size of the left triangle. B. Yes. All scalene triangles are similar C. No. Side c is not necessarily 24. D. No. Scalene triangles are never similar. The image projected on the screen at a movie theatre is 50 m wide. If the lm used in the projector is 50 mm, what is the scale factor of the projection? A. 33. 1 34. 1 10 B. 10 C. 100 D. 1000 35. Which pair of triangles are always similar? A. 2 scalene B. 2 equilateral C. 2 isosceles D. 2 obtuse Which of the following statements must be true? I. 36. All isosceles trapezoids are similar. II. All regular pentagons are similar. Which of these statements, if true, is su cient to prove that triangles LMN and NMO are similar? III. All parallelograms are similar. IV. All trapezoids are similar. A. I only B. II only C. IV only D. I and II only page 12 A. LN = 2 OM B. NO bisects LM C. OL = OO D. OMLN = OMNO Midterm Review 37. In the gure, OR = OC. 39. Which of these statements, if true, is su cient to prove that triangles CAT and RAM are similar? A. RA ? CM B. T is the midpoint of RA C. CA = 2 AM D. CT + TA = RM + MA 40. 38. Given that triangle ABC is similar to triangle DEC, OBAC corresponds to: A. OCDE B. ODEC C. OACB D. OECD page 13 In the gure, DE k BC. Which proportion is not true? A. AD AE = BA CA B. AD AB = AE AC C. DB BA = EC CA D. AD AE = DB AC Based on this gure, how many similar triangles can be identi ed? A. 2 C. 4 D. B. 3 cannot be determined Midterm Review 41. Complete the following proof. Given: AB = BC D is the midpoint of AB E is the midpoint of CB Prove: AE = DC statement reason 1. AB = BC given 2. DB = 12 (AB) defn. of midpoint 3. BE = 12 (BC) defn. of midpoint 4. both 1 2 of equal lengths 5. mOB = mOB 6. 7. AE = DC 42. Given: AE ? DB CF ? DB mOBAE = mODCF Prove: AB k DC Statements Reasons page 14 Midterm Review 43. Bisect OABC using a compass and straightedge. 44. Construct a line through point P perpendicular to line `. 45. Bisect the line segment AB. A page 15 B Midterm Review 46. Given: LF = KF LA = KA Prove: LJ = KJ statement 47. Given: AB = AC Prove: O3 = O4 reason statement 1. AB = AC reason 1. page 16 Midterm Review 48. Given the gure, how many triangles are similar to ADG? Name them. 50. In the diagram, AB = CB and BD bisects AC. a) Which congruence relationship justi es that ^ABD = ^CBD ? b) Why does mOA = mOC ? 49. RHOM is a rhombus. A, B, C, and D are the midpoints of each side. Prove that ABCD is a rectangle. page 17 Midterm Review