Geometry Semester Exam Review

Geometry – Semester Exam Review  GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day.  DO NOT FALL BEHIND. Do the problems that are assigned every night and come to class prepared to ask about the things you could not do.  GET SERIOUS. The grade you earn on this exam is worth 20% of your semester grade.  MAKE NOTES AS YOU WORK. As you do these problems, you will come across formulas, definitions, problems, and diagrams that you will want to put on your notecard.  NOTECARD: Your notecard must be in your own writing. You may put on it anything you think will help you on the exam. You may use the front and back. You will turn it in with your exam. You may also use your chart from Chapter 6.  There is nothing on the exam that you have not studied this year.  You will turn in your review packet on the day that you take your midterm.  This packet is worth a 1-weight quiz grade. This grade is based on:  Completion. I will check each day to make sure that day’s work is done.  Correctness. I will check random problems to make sure they are correct, or that you made corrections as needed.  Participation. I will keep track of people who ask questions, answer questions or put problems on the board. Everyone needs to participate at least three times. Geometry - Ch. 1 Review Name: _________________________ MATCHING...Answers will be used more than once. A. Collinear 1. _______ Like a dot. Indicates a location. 13. _______ Segments with the same length are ____. 2. _______ Flat, goes forever in all directions. 14. _______ Two little segments add up to the big segment. 15. _______ Two little angles add up to the big angle. 16. _______ Angle that measures exactly 90 C. Line 17. _______ Angle that measures less than 90 G. Segment 3. _______ Has two endpoints. A piece of a line. 4. _______ Straight, goes forever in two directions. 5. _______ Starts at one point and goes forever in one direction. 18. _______ Angle that is more than 90 but less than 180 6. _______ Two points determine a _______. B. Coplanar D. Plane E. Point F. Ray(s) H. Congruent I. Parallel 19. _______ Angle that measures exactly 180 7. _______ Three non-collinear points determine a ___. 20. _______ Unit of measure to measure angles 8. _______ Points on the same line are ____. 21. _______ Instrument used to measure angles 9. _______ Points on the same plane are ____. J. Segment Addition Postulate K. Angle Addition Postulate 22. _______ The sides of an angle are called ______. 10. _______ Two lines intersect in a ____. L. Acute M. Degree N. Obtuse 11. _______ Two planes intersect in a ____. O. Protractor P. Right 12. _______ Two lines that never intersect are ______. Q. Straight Fill in the blank with the correct word. 23. How many endpoints are on a line? ___________on a segment?___________on a ray? ___________on a plane?___________ 24. Do we ever use three letters to name a segment, line or ray? __________ Careful...this is a common error on the test! 25. When naming a ray, which letter always goes first? __________________ 26. How many lines can you draw through one point? _________ picture: 27. What about two points? _________ picture: Use the diagram to name the following. Use proper notation! 28. In the diagram, name two different rays that go through point A __________________________ 29. Now, state two different ways to name the ray having endpoint A __________________________ 30. List three points __________________________ 31. How many points are on this line? ____________ 32. List three different segments ________________ 33. Name the longest segment ________ 34. List three different ways to name this line __________________ 35. Use the next picture to name the plane two different ways ___________________________ 36. List three points on this plane ________________37. How many points are on this plane? _____________________ Use the diagram to determine if these are the same. Answer yes or no. 38. MA and AN _____ 39. AN and MA _____40. MA and AM _____ 41. NA and NM _____ Use the diagram to name the intersection of each pair of lines. 42. DB and EF _____43. FG and CD _____ 44. ED and CF _____ 45. BF and ED ______ * 46. The name for two coplanar lines that do not intersect is _____________ Are B, C and D collinear? ____C, F, D? ______ Use the diagrams to name the intersection of each pair of planes. 47. R and S _______ 48. U and T _______ 49. R and T _______ 50. R and U _______ 51. Since R and U don’t intersect, they are called ______________ 52. In the next picture, the plane that contains lines a and b is______ 53. The intersection of planes P and S ____________ .B 54. How many points are in the intersection of these planes? _______Are K, F, Q, and D coplanar? _______ Are B, F, Q and D coplanar? ____ Use the Segment Addition Postulate to find each length. 55. 56. 57. 40 5x - 1 22 25 NQ = ___________ GH= ___________ 58. XZ = ___________ 59. 60. 2x - 4 3x - 4 RT = ___________ LM = ___________ FG = ___________ Use the Segment Addition Postulate to write an ALGEBRAIC EQUATION. Then, solve the equation for x. 8x + 9 32 27 61. 62. 63. Equation____________________________________ Equation____________________________________ Equation____________________________________ x = ___________ x = ___________ x = ___________ Use the pictures to match two PAIRS of congruent segments. Use the correct notation to write a congruence statement. 64. Congruence statement pairs: ________________________ ________________________ J K Given the picture, state the measure of each angle or write the measure in the proper location on the diagram. 65. 66. 67. 68. m VEZ  _____ m PRT  _____ m TRS  ____ m REU  _____ m VEU  _____ m YXZ  10 m WXZ  60 m WXY  50 m 1  110 m 2  70 m3  110 m 4  70 Find the measure of each angle using addition or subtraction. 69. m RSP = 20 m PST = 30 70. m ABD = 120 mABC = 35 71. m TOS = 150 m TOR = _________ m RST = _______ m CBD = _______ m SOR = _______ 72. m EFH =15 73. m PQR = 23 74. m RQS = 57 m EFG = _________ m PQS = _____ m PQS = _____ m HFG = _______ m RQS= _______ m PQR = _______ Write an ALGEBRAIC EXPRESSION for the given angle. 75. m ADC= __________ 76. m NRQ= ____________ Write an ALGEBRAIC EQUATION for the given angle and solve. 77. mKLM = _________ 78. m VRS= _______ Equation: ________________________________ Equation: _______________________________ x = _________ x = _________ m KLN = _______ m NLM= _______ m VRT = _______ m TRS = _______ 79. 80. 81. 79. 80. 81. 82. 83. 84. 82. 83. 84. 85. 86. 87. 85. 86. 87. Geometry - Ch. 2 Review Name: ____________________________ Fill in the blank with the missing term. 1. Two angles that add up to 180°._____________ Terms: 2. Ray that divides an angle into two congruent angles.__________ Complementary Angles 3. A segment, line, ray or plane that intersects a segment at its midpoint.______________ Supplementary Angles 4. The point right in the middle of a segment.__________ Midpoint 5. Two angles that add up to 90°. ___________ Adjacent Angles Segment Bisector 6. Two angles that make a straight line. __________ Angle Bisector 7. Angles next to each other that share a common side and vertex. ____________ Linear Pair 8. Angles across from each other that are always equal. _________ Vertical Angles 9. When a conclusion is reached based on FACTS. __________ Inductive Reasoning Deductive Reasoning 10. When a conclusion is reached based on a PATTERN. ____________ 11. Draw the midpoint of and label it X, then name the resulting congruent segments. 12. M is the midpoint of . Write an equation, solve for x, and find the indicated lengths. 13. Use the Midpoint Formula to find the coordinate of the midpoint. (-7, 5) and (5, 3) Midpoint: ( The congruent segments are:__________ A segment has _____ midpoint(s). , ) x= _______ JM= _________ MK=________ 14. Draw and label three bisectors of this segment. 15. Notice the bisector and corresponding tick marks. Find the indicated lengths. 16. Notice the bisector and corresponding tick marks. Find the indicated lengths. AC = 150 yards CB= _________ AB=__________ AB= ___________ BC=___________ A segment has _____ bisectors 17. 18. bisects ∠ABC 19. bisects ∠XYZ m∠1 = 56° m∠2=_________ m∠ABC= _________ m∠XYZ = 56° m∠1=_________ m∠2= _________ 20. Given that is the bisector of ∠ABC, write an ALGEBRAIC EQUATION and solve. 21. Given that is the bisector of ∠XWY, write an ALGEBRAIC EQUATION and solve. 22. Name the adjacent angles in this picture. Y=______m∠ABD=_______ m∠ABC=_____ 23. 24. x=______m∠XWZ=_______ m∠ZWY=_____ 25. Adjacent angles:_________ These angles add up to ______ m∠1=_____ These angles add up to ______ m∠1=_____ 28. 29. Name the bisector of this angle. _______ Name the congruent angles: ________ 15° Complement: Supplement: 26. 172° Complement: Supplement: 27. m∠1=_______ m∠2=_______ These angles are ____________ m∠1=_____ m∠1=_______ m∠2=_______ m∠3=______ m∠3=_______ m∠4=_______ 30. m∠1 = ______ m∠2=______ m∠3 = ______ m∠4=______ 31. Determine whether the angles are vertical, complementary, supplementary or none of these. ∠4 and ∠5 _________________ ∠2 and ∠4 _________________ ∠3 and ∠4 _________________ ∠1 and ∠3 _________________ Given the picture, write an ALGEBRAIC EQUATION and solve for x. 32. These angles add up to _____ 33. These angles add are_____ 34. These angles add up to _____ Equation: Equation: Equation: x= _____ m∠ABD=______ m∠DBC=______ x = _______ x = _______ Underline the hypothesis once, and circle the conclusion. 35. If I pass my driver’s test, then I will get my license. 36. If this is Homecoming Week, then there will be an assembly on Friday. Decide whether this is an example of inductive or deductive reasoning. 37. The sun is a star, the sun has planets; therefore some stars have planets. 38. There has been a float party every night this week, therefore tonight will be a float party. Give a counterexample to show that each statement is false. 39. All GP students are sophomores. _______________________________________________ 40. All quadrilaterals are rectangles. ________________________________________________ Write next three numbers in the pattern 41. -5, -1, 3, 7, ______, _______, _______ 42. 2, 3, 5, 8, 12, ______, ______, ______ 43. Conditional: If a quadrilateral has four right angles, then it is a rectangle. Converse: __________________________________________________________________________ True or False Inverse: __________________________________________________________________________ True or False Contrapositive: __________________________________________________________________________ True or False What can you conclude from the true Statements below? 44. If you wash your cotton t-shirt in hot water, It will shrink. You wash your cotton t-shirt in hot water. Write a single if-then statement that follows from the pair of true statements below. 45. If the ball is thrown at a window, it will hit the window. If the ball hits the window, then the window will break. Therefore, _________________________________ ______________________________________________ 46. Multiple Choice: What is the next figure in this pattern? Geometry – Ch. 3 Review Name _______________________________ State the following using the picture. Don’t forget to use angle symbols! 1. Four interior angles ________, ________, ________, ________ 2. Four exterior angles ________, ________, ________, ________ 3. Two pairs of alternate interior angles _______ & _______, and _______ & _______ 4. Two pairs of alternate exterior angles _______ & ______ , and _______ & _______ 5. Four pairs of corresponding angles _______ & ______, _______ & _______, _______ & _______, and _______ & ______ 6. Four pairs of vertical angles _______ & _______, _______ & _______, _______ & _______, and _______ & _______ Choose the letter that shows the correct relationship between the angle pairs. 7.  3 and  9 ____ 8.  1 and  12 ______ 9.  8 and  13 ____ 10.  2 and  10 ______ 11.  5 and  7 ____ 12.  6 and  16 ______ 13.  1 and  2 ____ 14.  5 and  13 ______ r A. alternate interior s m B. same-side interior C. alternate exterior D. same-side exterior E. corresponding F. vertical l 15.  10 and  16 ____ G. linear pair 16.  13 and  15 ______ Describe the relationship between the pairs of angles by circling the word that makes the sentence true. supplementary the corresponding angles are: congruent supplementary the same side interior angles are: congruent supplementary 17. If lines are parallel, then ….the alternate interior angles are: congruent 18. Vertical angles are always congruent supplementary even if the lines are not parallel. 19. Angles that are a linear pair are always congruent supplementary even if the lines are not parallel. Find the measure of all the angles shown in the picture. 50 20. 21. 24. 150 22. 25. JKLM is a parallelogram 1 30 2 40 26. 4 3 23. 27. 80 42 70 2 This is a trapezoid. 1 60 51 1 _____ 2 _____ K _____ L _____ 3 _____ 4 _____ M _____ H _____ F _____ 1 _____ 2 _____ 28. ROCK is a parallelogram 29. STAR is a parallelogram 30. PLAY is a parallelogram O ______ C ______ R ______ A ______ 1 ______ PLA ______ K ______ S ______ 2 ______ 3 ______ 31. SONG is a parallelogram 32. 33. Hint: There are 180 in a triangle! 1 ______ 2 ______ SGN ______ 1 ______ 2 ______ 1 ______ 3 ______ 4 ______ 3 ______ 4 ______ 5 _______ 3 ______ 2 ______ 4 ______ State the type of angles shown and find the measure of 1. 34. 35. 36. 37. 38. Type of angles ______________ Type of angles ______________ Type of angles ______________ Type of angles ______________ Type of angles ______________ 1 ______ 1 ______ 1 ______ 1 ______ 1 ______ Use the relationship between the angles given to write an equation and solve for x. 39. 40. 41. Type of angles _______________________ Type of angles _______________________ Type of angles ____________________ Relationship: congruent or supplementary Equation: Relationship: congruent or supplementary Equation: Relationship: congruent or supplementary Equation: x = ________ x = ________ x = ________ 42. 43. 44. Relationship: congruent or supplementary Equation: Relationship: congruent or supplementary Equation: Relationship: complementary or supplementary Equation: x = ________ x = ________ x = ________ 45. The SYMBOL for Parallel is: ____________ The SYMBOL for Perpendicular is __________ Determine whether enough information is given to conclude that the lines are parallel. If so, state the reason. Choices are:  Alternate Interior Angles Converse (AIA)  Alternate Exterior Angles Converse (AEA)  Same-Side Interior Angles Converse (SSI)  Corresponding Angles Converse (CA)  Not enough proof that the lines are parallel. 46. 47. 48. 132。 49. 40 50. 40 Circle the segments or lines that must be parallel. n m 51. 52. 53. 。 88 x 。 88 Choices: SW || MI or SM || WI Choices: IH || FG or FI || GH Choices: 。 87 y m || n or x || y Fill in the blank with PARALLEL, PERPENDICULAR, or INTERSECTING to make each statement true. 54. Line q is ____________________ to line r 55. Line p is ____________________ to line r 56. Line p is ____________________ to line q 57. Line p is ____________________ to line s Consider each segment in the diagram at the right as part of a line. Complete the statement. 58. Name three segments parallel to TZ . ____________________________ 59. Name four segments that intersect TZ . __________________________ 60. Name four segments skew to TZ . _______________________________ Complete the theorems about parallel, perpendicular and skew lines. 61. All right angles are _________________. 62. If two lines are perpendicular, then they intersect to form four _________________. 63. Two lines are parallel lines if they lie in the same plane and do not _________________. 64. Two lines are perpendicular lines if they intersect to form a _________________ angle. Choices: CONGRUENT INTERSECT PARALLEL PLANE RIGHT RIGHT ANGLES 65. Two lines are skew lines if they do not lie in the same _________________ and do not intersect. 66. Two planes are _________________ planes if they do not intersect. 67. Draw a segment through Z parallel to JK (symbols!) 68. Draw a segment through Z perpendicular to JK (symbols!) ·Z J ·Z K J K Fill in the blank with a number. 69. Parallel Postulate If there is a line and a point not on the line, then there is exactly _________ line through the point parallel to the given line. 70. Perpendicular Postulate If there is a line and a point not on the line, then there is exactly _________ line through the point perpendicular to the given line. Describe the relationship between the lines shown. (intersecting, parallel, skew) 71. lines w and k 72. lines j and k 73. lines m and k 74. lines u and w 75. lines m and n Geometry Chapter 4 Review Name:__________________________________________ MATCH each type of triangle with its definition. Equilateral Triangle _____ Equiangular Triangle _____ A. Triangle with one right angle. E. Triangle with one obtuse angle. Isosceles Triangle _____ Acute Triangle _____ B. Triangle with all (3) equal sides. F. Triangle with two equal sides. Scalene Triangle _____ Right Triangle _____ C. Triangle with all (3) equal angles. G. Triangle with no equal sides. Obtuse Triangle _____ D. Triangle with three acute angles. Classify the triangle by its sides. 1. 2. 3. 4. 7. 8. Classify the triangle by its angles AND sides. 9. 10. 11. 12. Sides: equilateral isosceles scalene Sides: equilateral isosceles scalene Sides: equilateral isosceles scalene Sides: equilateral isosceles scalene Angles: acute obtuse equiangular right Angles: acute obtuse equiangular right Angles: acute obtuse equiangular right Classify the triangle by its angles. 5. 6. Identify the side opposite each angle. 13. Use the picture to name the following. Angles: acute obtuse equiangular rt. Name the equal sides and equal angles in each picture. 14. 15. 16. Side opposite X: ________ Side opposite Y: ________ Legs______________ Base _______ Equal sides: _______________ Side opposite Z: ________ *Use correct notation! Vertex angle _______ Base angles ___________ Equal angles: ______________ Equal angles: ______________ Using ABC, name the following. 17. The interior angles of this triangle are ____________________ Equal sides: _______________ The sum of the interior angles is ______ degrees. 18. The exterior angle of this triangle is _______ The adjacent interior angle (next to the exterior angle) is _______ 19. The exterior and the adjacent interior angle add up to ______degrees. The remote interior angles shown are ___________ 20. The sum of the remote interior angles is equal to ______________________________ Find the measure of each angle. 21. m1 = ______ 22. m1 = ______ 23. m1 = ______ 24. m1= ______ m2= ______ Each angle in an equiangular triangle is ____ degrees. 25. m1 = _____ m2 = _____ 26. m1 = _____ 27. m1= ____ m3= _____ 28. m1 = ____ m2= ______ m3= ______ m4= ______ m5= ______ 29. x = _____ 33. m8 = ______ m9 = ______ 30. x = _____ 34. m3 = ______ m4 = ______ 31. m1 = _____ m2 = _____ 32. m1 = _____ m2 = ____ 35. m2 = ______m1 = ______ 36. m1= ______m2 = _____ m5 = ______ Write an algebraic equation for each triangle and solve for x. 37. 38. 39. Equation: Equation: Equation: x = _______ x = _______ x = _______ 40. 41. 42. Equation: Equation: y = ______  Equation: x = ______ x = ______ State the Pythagorean Theorem:___________________ What is it used for?__________________________________________ Use the Pythagorean Theorem to find the following missing side. An equation must be given! Round decimals to the nearest 100th. 43. 44. 45. x x Equation: Equation: x = ______ 46. x Equation: x = ______ 33 x = ______ 47. 48. x 17 x 13 x Equation: x≈ ________ Equation: x≈ ________ Equation: x≈ ________ 49. A 20-foot ladder is leaning against a wall. It reaches up the wall 16 feet. How far is the bottom of the ladder from the wall? 50. A 26-ft wire is attached to an electrical pole. The wire attaches to a stake on the ground. If the stake is 10 feet from the base of the pole. How tall is the pole? Equation: Equation: 51. Find the length of the diagonal of a square if each side 10 cm. 52. Mary hikes 7 km north and 5 km west. How far is she from her starting point? Equation: Equation: Can the given side lengths make a right triangle. Circle yes or no. You MUST support your answer with an equation! 53. 4 ft, 9 ft, 7 ft 54. 10 in., 26 in., 24 in. 55. 20 cm, 16 cm, 12 cm 56. 20 in., 28 in., 21in. Equation: Equation: Equation : Equation: yes or no yes or no yes or no yes or no Given the Pythagorean Triple, state THREE OTHER MULTIPLES that are also Pythagorean Triples. 57. 3, 4, 5 58. 5, 12, 13 59. 8, 15, 17 Find the DISTANCE between the two points. Round your answers to the nearest 100th, if necessary. 60. 61. 62. ( -2, 1 ) and ( 3, 2 ) d= x  x 2   y  y 2 63. ( -1, 2 ) and ( 3, 0 ) Matching: 64. A segment from a vertex to the midpoint of the opposite side _____ A. Altitude 65. A segment from a vertex perpendicular to the opposite side _____ B. Angle Bisector C. Median 66. A segment from a vertex that bisects the corner angle _____ D. Perpendicular 67. Cuts a segment in half and makes a 90 angle _____ Bisector BD is a MEDIAN of ABC. Find each length. 68. 69. 70. AD = _______ AC = _______ AD = _______ DC = _______ AD = _______ AC = _______ 71. The medians on this picture are segments: ____________________________ Draw and label the MEDIAN from vertex X. 72. 73. . x Fill in the blank. 74. If a point is on the angle bisector, then it is ___________________________ from the two sides of the angle. Write an equation and solve for x. 75. 76. 77. Equation: Equation: Equation: x = _____ x = _____ PS = _____ RS = _____ x = _____ PM = _____ MN = _____ 78. If a point is on the perpendicular bisector of a segment, then it is __________________ from the endpoints of the segment. Write an equation and solve for x. 79. 80. Equation: x = _____ BC = _____ 81. Equation: DC = _____ x = _____ AB = _____ Equation: CB = _____ x = _____ AD = _____ CD = _____ Write an equation and solve for x. 82. XY is the angle bisector of X. 83. PS is a median. Equation: Equation: x = _____ x = _____ Fill in the blanks: _______ sides are across from BIG angles, _______ sides are across from LITTLE angles and________ sides are across form EQUAL angles. List the ANGLES in each triangle from smallest to largest. List the SIDES of each triangle from shortest to longest 84. 86. 85. 87. Find mJ first. __________________ __________________ __________________ __________________ 88. Triangle Inequality Theorem: The sum of any two sides of a triangle must be …__________________________________________ Can the following side lengths make a triangle? Circle yes or no. Explain all answers! 89. 1 cm, 2 cm, 3 cm _____________________ yes or no 90. 2 mm, 3 mm, 4 mm____________________ yes or no 91. 8 cm, 8 cm, 8 cm _____________________ yes or no 92. 9 mm, 9 mm, 18 mm ___________________ yes or no 93. 21 m, 4 m, 13 m______________________ yes or 95. Draw and label the ANGLE BISECTOR of X. 94. 50 cm, 50 cm, 25 cm___________________ no 97. X 96. Draw and label the PERPENDICULAR BISECTOR of 41. 98. AB. A B yes or no Geometry Ch. 5 REVIEW Name ___________________________ 1. What does it mean for two triangles to be congruent? ____________________________________________________________ Study the picture to name all the pairs of corresponding sides and angles. Order of the letters matters! 2. Pairs of Corresponding Sides Pairs of Corresponding Angles 3. Pairs of Corresponding Sides Pairs of Corresponding Angles CD  ________ C  ______ XZ  ________  X  _______ EC  ________  D  ______ YX  ________ Y  _______ ZY  ________  Z  _______  ZXY   _______  E  ______ DE  ________  ECD   _______ Congruence Statement: Congruence Statement: 4. Mark each pair of corresponding angles and corresponding sides to show the congruent parts.  PQR   ABC 5. CPCTC stands for: ___________________ Parts of ___________________ Triangles are _____________________. Given  ABC   DEF , find the missing length or angle measure. 6. 7. 8. Hint: How many degrees are in a triangle? DE  _____ BC  _____ AC  _____ mB = _____ mF = _____ mA = _____ Hint: How many degrees are in a triangle? DE  _____ BC  _____ DF  _____ mA = _____ mF = _____ mB = _____ Mark the triangles to correspond to each postulate: 9. SSS 10. SAS 11. ASA EF  _____ ED  _____ CA  _____ mD = _____ mF = _____ mE = _____ 12. AAS 13. H-L OR Name the postulate which could be used to show the triangles are congruent. Don’t forget to mark "free" sides and angles! Fill in the congruence statement where indicated. Choices are: SSS, SAS, ASA, AAS, H-L or none. 14. 15. 16. 17. Postulate __________ Postulate __________ Postulate __________ Postulate __________ MON   ________ PQR   ________ LJK   ________ FED   ________ 18. 19. 20. 21. Postulate __________ Postulate __________ Postulate __________ Postulate __________ STR   ________ ZYX   ________ ADC   ________ ADC   ________ 22. 23. 24. 25. Postulate __________ Postulate __________ Postulate __________ Postulate __________ ABC   ________ PQR   ________ KJM   ________ UHS   ________ U Mark the pictures first and then state what postulate proves the triangles congruent. Choices: SSS, SAS, ASA, AAS, H-L or none. 26. AB  MN and ; A  M 27. B  N Postulate __________ AB  MN and ; A  M 28. C  O AB  MN ; AC  MO and Postulate __________ 29. BC  NO AB  MN ; BC  NO and Postulate __________ B  N Postulate __________ Using the given information and method, state the PAIRS of additional information needed to prove the triangles congruent. 30. BC  YZ ; C  Z AAS Postulate 31. BC  YZ ; C  Z ; SAS Postulate Pair of sides or angles needed__________________ Pair of sides or angles needed__________________ 33. BC  EC ; SAS Postulate 34. AC  XZ ASA Postulate 32. BC  YZ ; C  Z ASA Postulate Pair of sides or angles needed__________________ 35. AC  XZ SSS Postulate (Hint: Mark "free" angles!) Pair of angles needed__________________ Pair of sides needed_____________ 36. AB  XY ; SAS Postulate Pair of angles needed__________________ Pair of sides needed__________________ Pair of sides needed__________________ (TWO solutions) (Hint: Mark given sides… each solution has a pair of sides and a pair of angles.) OR ONE WAY: THE “OTHER WAY”: Pairs of sides needed__________________ Pairs of sides needed__________________ Pairs of angles needed__________________ Pairs of angles needed__________________ 37. AB  XY ; AAS Postulate (TWO solutions) (Hint: Mark given angles… each solution has a pair of sides and a pair of angles.) ONE WAY: OR THE “OTHER WAY”: Pairs of angles needed__________________ Pairs of angles needed__________________ Pairs of angles needed__________________ Pairs of angles needed__________________ Is the segment a LEG or the HYPOTENUSE ? 38. 39. 40. FE _____________ FD _____________ DE _____________ Name the ANGLE that is included between the two sides. 41. CD and BC ________________ 42. AB and CB _______________ 43. DC and BD ________________ 44. AB and BD ________________ Geometry Review - Ch. 6 Name __________________________________ For each of the following shapes, state the definition, draw a picture, and choose the letter that corresponds to the properties. Parallelogram Definition: _________________________________________ CHOICES FOR PROPERTIES: Picture: Properties: 1. ______ 2. ______ 3. ______ 4. ______ A. Opposite sides are congruent B. Opposite angles are congruent C. Consecutive angles are supplementary Rhombus D. Diagonals bisect each other Definition: _________________________________________ Picture: Properties: 1. ______ 2. ______ 3. ______ 4. ______ E. Diagonal bisect the corner angles F. Diagonals are congruent G. Diagonals are perpendicular 5. ______ 6. ______ Rectangle Square Definition: _________________________________________ Definition: _________________________________________ Picture: Picture: Properties: 1. ______ 2. ______ 3. ______ 4. ______ Properties: 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 5. ______ 6. ______ 7. ______ Study the Venn Diagram which relates all of these quadrilaterals.. Trapezoid Definition: _________________________________________ Picture: An isosceles trapezoid has _____________________________ The base angles of an isosceles trapezoid are ______________ To find the length of the midsegment, you _______ the bases together and divide by ______. Answer true or false. 1. Every rectangle is a square ______________________ 2. Every square is a rectangle ___________________________ 3. Every parallelogram is a rhombus_________________ 4. Every rhombus is a rectangle__________________________ 5. Every square is a quadrilateral____________________ 6. Every square is a rhombus ____________________________ 7. The diagonals of a rectangle are perpendicular _______ _____________ 9. The diagonals of a rectangle are congruent ___________ _______________ 8. The diagonals of a square are perpendicular 10. The diagonals of a rhombus are congruent 11. The opposite sides of a parallelogram are congruent________ 12. The opposite angles of a parallelogram are supplementary_______ 13. The diagonals of all parallelograms bisect each other _______ ________ 14. The diagonals of all parallelograms are congruent Name the following segments or angles in the trapezoid. Use the correct notation! 15. Two Bases: ____________ 16. Two Legs: ____________ 17. Midsegment: ____________ 18. Two pairs of Base Angles: _________ & _________ For each PARALLELOGRAM, find each length or measure. 19. 20. 21. A mC ______ mB ______ m1 ______ m2 _____ XO______ XZ _____ BC = ______ DC = ______ m3 ______ m4 _____ OY ______ WY _____ For each RHOMBUS, find each length or measure. 22. 23. 24. mC ______ mB ______ m1 ______ m2 _____ m1 ______ m2 _____ BC = ______ DC = ______ m3 ______ m4 _____ m 3 ______ m4 _____ For each RECTANGLE, find each length or measure. 25. 26. 27. m1 ______ m2 ______ m1 ______ m2 _____ XO_____ XZ _____ OY _____ BC = ______ DC = ______ m3 ______ m4 _____ WY _____ m1 ____ m2 ____ For each SQUARE, find each length or measure. 28. 29. 30. m1 ______ m2 ______ m1 ______ m2 _____ m1 ______ m2 _____ BC = ______ DC = ______ m3 ______ m4 _____ m3 ______ m4 _____ m2 _____ For each TRAPEZOID, find each length or angle measure 31. 32. mR ______ mT ______ 33. mP _____ mS ____ m1 ______ mA _____ PA _____ m3 _____ m4 ______ y = ______ Name all the quadrilaterals that have each property. Choices: parallelogram, rhombus, rectangle, square. There will be more than one answer! 34. All angles congruent _______________________________________ 35. Opposite angles are congruent _______________________________________ 36. The diagonals are perpendicular ______________________________ 37. The diagonals bisect each other ______________________________________ Using the properties of each shape to write and solve an algebraic equation for each picture. Rhombus Parallelogram 38. Rectangle 39. 40. Equation: Equation: Equation: x = _______ mABC = ______ mBCD = ______ x = _______ x = _______ Square Trapezoid IsoscelesTrapezoid 41. 42. 43. Equation: Equation: Equation: x = _______ x = _______ x = _______ MATCH the name of each polygon with the number of sides. 44. Decagon 45. Octagon A. 3 sides 46. Quadrilateral 47. Hexagon E. 7 sides B. 4 sides F. 8 sides 48. Nonagon 49. Pentagon C. 5 sides G. 9 sides 50. Heptagon 51. Triangle D. 6 sides H. 10 sides 55. 56. Classify (Name) the polygon by its number of sides. 52. 53. 54. 57. Name the following for the pentagon shown. 58. Two sides adjacent to RS _______________ 59. Two vertices consecutive to T ______________ 60. Two angles consecutive to T ____________ 61. Two diagonals with endpoint R _____________ 66. The sum of the angles of a TRIANGLE is ________ 67. The sum of the angles of a QUADRILATERAL is ________ Use the formulas to find the measure of the missing angle. 62. 63. 64. 65. m1= ______ mD= ______ mD= ______ m1= ______