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Transcript
GEOMETRY STUDY GUIDE FOR FALL SEMESTER FINAL CHAPTERS 1 - 7 Indicate the best answer by writing the appropriate letter. 1. If M is between R and T then ___?___. A) MR + RT = MT B) RM = MT C) RM + MT = RT 2. The two angles in a pair of vertical angles are always __?__. A) congruent B) adjacent C) acute D) MR = RT D) and acute 3. If two angles are complementary to the same angle, then they are __?__ to each other. A) complementary B) vertical C) adjacent D) congruent 4. In a plane, two lines perpendicular to the same line are __?__ parallel. A) always B) sometimes C) never 5. Two lines parallel to the same plane are __?__ parallel to each other. A) always B) sometimes C) never 6. Which of the following is the hypothesis of the conditional: I’ll stay if I win. A) I’ll stay. B) I win. C) I’ll leave if I lose D) I’ll win if I stay. 7. Choose the statements that must be true for a rhombus. I. The diagonals are congruent . II. The diagonals bisect each other. III. The diagonals are perpendicular. IV. The diagonals bisect the angles. 8. Choose the statement that must be true for a rectangle. I. The diagonals are congruent . II. The diagonals bisect each other. III. The diagonals are perpendicular. IV. The diagonals bisect the angles. 9. If CAT DOG, then which of the following are true? I. A O II. AT = DO III. TC = GD IV. CTA DGO r 1 4 Use for problems #10 - 12 10. If r || s, then 1 __?__. A) 9 B) 11 C) 5 D) 9 and 5 11. If 3 12, then __?__. A) b || c B) r || s 12. If b || c, then 6 must be __?__ to 3 A) congruent B) supplementary 5 7 s 3 6 11 13 8 C) b || c and r || s 9 2 16 10 12 14 b c 15 D) none of these C) congruent and supplementary D) adjacent 13. If two angles of a triangle measure 47 and 93, then the measure of the third angle is __?__. 14. The measures of the angles in a triangle are in the extended ratio 2: 4: 9. Find the measure of the largest angle. 15. The diagonals of a trapezoid __?__ bisect each other. A) always B) sometimes C) never 16. If the lengths of two sides of a triangle are 7 and 13, then the length of the third side must be between _?_ and _?_. 17. In ABC, mA = 4x + 5, mB = 2x + 20, and mC = 5x – 10. The two congruent sides of the triangle are __?__. A) AB and AC B) AB and BC C) AC and BC D) AB , BC , and AC 18. If ABCD is a parallelogram, then which of the following must be true? A) A D B) AB DA C) AB BC D) mB+ mC = 180 19. A and B are supplementary, mA = 2n, and mB = 3n + 20. Find mB. 1 2 20. Given: a || b, m1 = 3x + 30; m3 = 2x. Find m4. 3 5 21. Which of the following is a false statement? A) Points A, B, and C are coplanar. B) Planes M and N intersect in DE C) Exactly one line contains points B and C. D) Exactly one plane contains point B and DE a Use for question #20. b 4 M A D E N C B 22. RING is a parallelogram. RI = x + 6, IN = 2x + 4, and NG = 3x. Find GR. R G I N 23. Which of the following could not be the lengths of the sides of a triangle? A) 1, 3, 2 B) 2.5, 5, 3 C) 4, 4, 4 D) 2, 3, 2 24. Which of the following is the converse of the statement: If A and B are right angles, then A B? A) B) C) D) If A and B are not right angles, then A B. If A B, then A and B are not right angles. If A and B are not right angles, then A B If A B then A and B are right angles. 25. What is the sum of the measures of the interior angles of a convex hexagon? 26. A regular polygon has 12 sides. What is the measure of each interior angle? 27. If RA = x and AK = 4x + 6, find the coordinate of the midpoint of AK . A R K 4 12 B 28. BD bisects ABC. mABD 4x 4 and mCBD 5x 1. Find the value of x. A D 29. Find the value of y. (6x – 20) (4y + 8) (3x + 10) C 30. Through a point not on a line, how many lines are parallel to the given line? 31. If XY || WZ , which pair of angles are congruent? Y A) 2 5 B) 3 6 C) 2 6 1 D) 8 4 8 X 32. Find x. 3 2 7 6 5 x 24 108 33. The median of a trapezoid measures 23 cm and one of the bases is 15 cm. Find another base. 34. Draw three types of lines in the space provided. A B 35. Complete the proof. Given: OA bisects BOF and Prove: mAOF = mEOF. O OB bisects AOC. F C D E Conclusions 1. OA bisects BOF and BD bisects AOC 2. mBOA = mAOF mBOC= mBOA 3. mBOC = mAOF 4. mEOF = mBOC 5. mAOF = mEOF Justifications 1. Given 2. ? 3. ? 4. ? 5. ? W Z 4