Geometry Test Review Sheet Answers

Geometry 1st Quarter Test Review Sheet Name: ________________________________ 1. Let B be between A and C. If AB = 3x + 5, BC = 5x – 1, AC = 36, then x = ___4____ AB+BC=AC 2. Let B be the midpoint of AC . If AB  2 x  6 , and BC  4 x  10 , then AB  ___22___ AB=BC x=8 3. Let 1 and 2 be complementary. If m1 = 4x + 3 and m2 = x + 2, m1 = ___71___ 1 + 2 = 90 4. Write the equation of a line through (1, 1) that is parallel to the line y = -5x + 7. y = -5x + 6 5. Write the equation of a line through (0, 3) that is perpendicular to the line y  1 x 2. 5 y = 5x + 3 6. Given: If it is raining, then the ground is wet. State the following: hypothesis: __It is raining ________________________________________________________ conclusion: __The ground is wet___________________________________________________ converse: __If the ground is wet, then it is raining. ___________________________________ inverse ___If it is not raining, then the ground is not wet. ____________________________ contrapositive: __ If the ground is not wet, then it is not raining.___________________________ 7. Write the conclusion for the syllogism: “If A, B, and C are distinct points on a circle, then they are not collinear. If three distinct points do not lie on the same line, then they always form a triangle.” If A, B, and C are distinct points on a circle, then they always form a triangle. 8. Given A(4,-9) and B (-2,6). a) Find the slope of AB . b) Find the midpoint of AB . 5 2 (1, 1 9. Classify the angles: 1, 8 _Alternate Exterior_ 3, 5 _Same Side Interior_ 2, 6 _Corresponding____ 4, 5 __Alternate Interior___ 3 5 7 3 ) 2 2 c) Find AB. DISTANCE! 261 4 6 8 10. In the figure from #9, if m3 = 5x - 30 and m7 = 4x + 10, then m3 = ____170º_____ m3 = m7 11. Find x. x = 10 2x – 9 12. Find x. x=5 4x +121 5x+14 x+1 13. Find the measure of DEF __30º________ D E (3x) (4x+20) F 14. Name 3 undefined terms. ___Point Line Plane_____________________________________ 15. Two planes intersect in a ___line____; two lines intersect in a __point______. 16. State the Linear Pair Postulate. __If 2 angles form a linear pair, then they are supplementary._________ 17. State the Reflexive Property. _a = a__________________ 18. Vertical angles are __congruent____. 19. All right angles are __congruent______. 20.Two angles that are supplementary to the same angle are __congruent to each other_________ 21. Define supplementary and complementary angles. __Supplementary = 180º Complementary = 90º________ 22. Sum of the measures of the angles in a triangle = __180º________. 23. The acute angles of a right triangle are ____complementary______. 24. The measure of any exterior angle of a triangle is equal to __the sum of the 2 nonadjacent angles________. 25. C is in the interior of ABD . If mABC = 3x+7, mCBD = 4x+9, and ABD = 44. Find: a) mABC = __19º____ b) mCBD = __25º____ mABC + mCBD = mABD 26. Use the following equations to answers 26a, 26b, and 26c below. 1 1 2 (a) y  7 x  11 (b) y   x  5 (c) y  x  7 7 3 Fill in the blanks with parallel, perpendicular, or neither. 26a) Lines (a) and (b) are __Neither___________ (d) y  3  7 x 26b) Lines (a) and (c) are ___Perpendicular_________ 26c) Lines (a) and (d) are ____ Parallel _______ 27. Name the property, postulate, or theorem. a) If mA  mB , then mB  mA ______symmetric__________________ b) If Y is between X and Z, the XY+YZ=XZ ____segment addition postulate__ c) If MN = OP and OP = YV, then MN = YV ____Transitive_______________ 28. Find the slope of the line passing through the points A(-4, -3) and B(7, -2). 1 11 29. Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither. 1 Line 1 passes through (-4, 6) and (0, 8). m = parallel 2 1 Line 2 passes through (1, -8) and (5, -6). m = 2 30. Determine whether AB  CD . A(2, 8), B(-1, 4), C(-2, 3), and D(-10, -3). DISTANCE! AB = 5 CD = 10 Not Congruent 31. The measure of the complement of an angle is five times the measure of the angle. Find the measure of the angle and its complement. m1 = 15º m2 = 75º 5x + x = 90 32. 1 and 2 are a linear pair. m1  73 . Find the m2 . m2 = 107 º 73 + x = 180 33. If AB=16 and AC=31, Find the length of BC . 34. Find k if line segment RT has a length of 5. 3k A B BC = 15 C 2k R AB + BC = AC S k=1 T 3k + 2k = 5 35. Let C be between D and E. Use the Segment Addition Postulate to solve for n. DC = 6n  10 CE = 5n  12 n=6 DC + CE = DE DE = 44 36. If mDOE  25, and mEOF  28. What is the measure of DOF ? 37. If mABC  70, mABE  30, and mEBD  mDBC . Find mEBD. A D E O E mDOF = 53º B F mEBD = 20º D C 38. If mECD  (2 x  8), mBCD  (7 x  7), and mECB  64. Find mECD and mBCD. E D B x = 7 mECD  22, mBCD  42, C 39. If r s, m3  (5 x  32) and m5  (4 x  40), find m5. 1 3 40. Given: m1  m3. Which lines must be parallel? _l1 and l2___ same side interior x = 12 m5  88 2 l1 r 4 5 6 7 8 l2 2 1 s 5 41. Find the value of x. m1 3 4 m2 42. Find the value of x. x = 33° 88° x° x = 120° 63° 125° 57° x° 43. Find the value of x. 44. Find the measure of A below. 100° x = 45 A = 137 92° x° 35° A 49° 46. If RPQ  JKL, then LJ  __ QR __ 45. Find the measures of all three angles of the triangle. x = 36, 52°,72°, 56° 47. Given: LMN  UVW . Complete the statements. (x+16)° a) UW  __ LN ____ (2x)° (x+20)° 48. Use the figure below. B C D A b) LMN  __ UVW ___  a) Name the intersection of planes ABCD and EFBA. ___ AB _____ b) Name two parallel planes. ADEH & BCFG, ABEF & CDGH, or ABCD & EFGH           c) Name two pairs of skew lines. AD & EF , AD & GH , BC & EF , BC & GH , CD & FG, G F E       CD & EH , AB & FG, AB & EH  H            d) Name two parallel lines. AB & CD, AB & EF , AB & GH , AD & BC , AD & FG, AD & EH       AE & BF , AE & DH , AE & CG