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Name:__________________________________ Hr: ______ 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. 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 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. Midterm Review Assignments Date Assignment Thursday 1/10 Chapter 1 Friday 1/11 Chapter 2 Monday 1/14 Chapter 3 Tuesday 1/15 Chapter 4 Wednesday 1/16 Chapter 5 Thursday 1/17 Chapter 6 2nd Hour Exam: Tuesday, January 22nd 9:45-11:15 3rd Hour Exam: Friday, January 25th 8:00-9:30 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 _______. 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 ____. B. Coplanar D. Plane E. Point F. Ray(s) H. Congruent I. Parallel 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 __________________________ 33. How many points are on this line? ____________ 31. List three different segments ________________ 35. Name the longest segment ________ 32. List three different ways to name this line __________________ 33. Use the next picture to name the plane two different ways ___________________________ 34. List three points on this plane ________________35. How many points are on this plane? _____________________ Use the diagram to determine if these are the same. Answer yes or no. 36. MA and AN _____ 37. AN and MA _____38. MA and AM _____ 39. NA and NM _____ Use the diagram to name the intersection of each pair of lines. 40. DB and EF _____41. FG and CD _____ 42. ED and CF _____ 43. BF and ED ______ * 44. 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. 45. R and S _______ 46. U and T _______ 47. R and T _______ 48. R and U _______ 49. Since R and U don’t intersect, they are called ______________ 50. In the next picture, the plane that contains lines a and b is______ 51. The intersection of planes P and S ____________ .B 52. 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. 53. 54. 55. 40 5x - 1 22 25 NQ = ___________ GH= ___________ 56. XZ = ___________ 57. 58. 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 59. 60. 61. 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. 62. Congruence statement pairs: ________________________ ________________________ J Use a protractor to measure each angle. Classify the angle as acute, right, obtuse or straight. 63. 64. K 65. 66. How do you know which number to use on the protractor?______________________________________________________________________ Given the picture, state the measure of each angle or write the measure in the proper location on the diagram. 67. 68. 69. 70. m VEZ _____ m PRT _____ m TRS ____ m REU _____ m VEU _____ 71. Give another name for the angle in the diagram. Circle whether the angle appears to be acute, obtuse, right, or straight. m YXZ 10 m WXZ 60 obtuse right straight JLK____________ acute obtuse right straight MKL____________ acute obtuse right straight JML____________ acute obtuse right straight m 1 110 m 2 70 m3 110 m 4 70 Look at the markings on each picture and state which angles are congruent. Write a congruence statement. 72. LKJ____________ acute m WXY 50 73. Find the measure of each angle using addition or subtraction. Do NOT use a protractor! 74. m RSP = 20 m PST = 30 75. m ABD = 120 mABC = 35 76. m TOS = 150 m TOR = _________ m RST = _______ m CBD = _______ m SOR = _______ 77. m EFH =15 78. m PQR = 23 79. m RQS = 57 m EFG = _________ m PQS = _____ m PQS = _____ m HFG = _______ m RQS= _______ m PQR = _______ Now write an ALGEBRAIC EXPRESSION for the given angle. 80. m ADC= __________ 81. m NRQ= ____________ Now write an ALGEBRAIC EQUATION for the given angle and solve. 82. mKLM = _________ 83. m VRS= _______ Equation: ________________________________ Equation: _______________________________ x = _________ x = _________ m KLN = _______ m NLM= _______ m VRT = _______ m TRS = _______ 84. 85. 86. 84. 85. 86. 87. 88. 89. 87. 88. 89. 90. 91. 92. 90. 91. 92. Geometry - Ch. 2 Review Name: ____________________________ Fill in the blank with the missing term. 1. Two angles that add up to 180°._____________ 2. Ray that divides an angle into two congruent angles.__________ 3. A segment, line, ray or plane that intersects a segment at its midpoint.______________ 4. The point right in the middle of a segment.__________ 5. Two angles that add up to 90°. ___________ 6. Two angles that make a straight line. __________ 7. Angles next to each other that share a common side and vertex. ____________ 8. Angles across from each other that are always equal. _________ 9. When a conclusion is reached based on FACTS. __________ 10. When a conclusion is reached based on a PATTERN. ____________ ̅̅̅̅ and label it 11. Draw the midpoint of 𝐴𝐵 x, then name the resulting congruent segments. The congruent segments are:__________ A segment has _____ midpoint(s). 14. Draw and label four of the bisectors of this segment. ̅̅̅. Write an 12. M is the midpoint of 𝐽𝐾 equation, solve for x, and find the indicated lengths. Terms: Complementary Angles Supplementary Angles Midpoint Adjacent Angles Segment Bisector Angle Bisector Linear Pair Vertical Angles Inductive Reasoning Deductive Reasoning 13. Use the Midpoint Formula to find the coordinate of the midpoint. (-7, 5) and (5, 3) Midpoint: ( , ) x= _______ JM= _________ MK=________ 15. Notice the bisector and corresponding tick marks. Find the indicated lengths. 16. Notice the bisector and corresponding tick marks. Find the indicated lengths. CB= _________ AB=__________ ⃗⃗⃗⃗⃗⃗ bisects ∠ABC 18. 𝐵𝐷 AB= ___________ BC=___________ ⃗⃗⃗⃗⃗ bisects ∠XYZ 19. 𝑌𝐴 m∠1 = 56° m∠2=_________ m∠ABC= _________ m∠XYZ = 56° m∠1=_________ m∠2= _________ ∠ABC, write an ALGEBRAIC EQUATION and solve. 21. Given that ⃗⃗⃗⃗⃗⃗ 𝑊𝑍 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. A segment has _____ bisectors 17. Name the bisector of this angle. _______ Name the congruent angles: ________ ⃗⃗⃗⃗⃗⃗ is the bisector of 20. Given that 𝐵𝐷 15° Complement: Supplement: 26. 172° Complement: Supplement: 27. m∠1=_______ m∠2=_______ These angles add up to ______ 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. ________________________________________________ MATCH each statement with its definition. Write next three numbers in the pattern 41. Conditional _____ 42. Converse ______ 43. Inverse ______ 44. Contrapostive ______ 45. -5, -1, 3, 7, ______, _______, _______ 46. 2, 3, 5, 8, 12, ______, ______, ______ 47. 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? 48. If you wash your cotton t-shirt in hot water it will shrink. You wash your cotton t-shirt in hot water. Therefore, _________________________________ 50. What is the next figure in this pattern? 49. 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, _________________________________ 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 C. alternate exterior D. same-side exterior E. corresponding F. vertical l 15. 10 and 16 ____ B. same-side interior G. linear pair 16. 13 and 15 ______ Describe the relationship between the pairs of angles by circling the word that makes the sentence true. 17. If lines are parallel, then ….the alternate interior angles are: congruent supplementary the corresponding angles are: congruent supplementary the same side interior angles are: congruent supplementary 18. Vertical angles are always congruent supplementary even if the lines are not parallel. 19. Adjacent supplementary angles are always congruent supplementary even if the lines are not parallel. Find the measure of all the angles shown in the picture. 20. 21. 50 24. 150 22. 25. JKLM is a parallelogram 1 30 2 40 26. 4 3 23. 27. 80 70 42 2 51 1 This is a trapezoid. 60 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. There is one of each type! 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. Find the value of x, given that j is perpendicular to k. Type of angles _______________________ Type of angles _______________________ Type of angles ____________________ 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. Look carefully at the numbers in each picture! n m 51. 52. 53. 。 88 x 。 88 Choices: SW || MI or SM || WI Choices: Choices: IH || FG or FI || GH 。 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. 65. Two lines are skew lines if they do not lie in the same _________________ and do not intersect. Choices: CONGRUENT INTERSECT PARALLEL PLANE RIGHT RIGHT ANGLES 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 ·Z J (symbols!) ·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. m1 = ______ 22. m1 = ______ 23. m1 = ______ 24. m1= ______ m2= ______ Each angle in an equiangular triangle is ____ degrees. 25. m1 = _____ m2 = _____ 26. m1 = _____ 27. m1= ____ m3= _____ 28. m1 = ____ m2= ______ m3= ______ m4= ______ m5= ______ 29. x = _____ 30. 33. m8 = ______ m9 = ______ 34. x = _____ 31. m1 = _____ m2 = _____ m3 = ______ m4 = ______ 32. m1 = _____ m2 = ____ 35. m2 = ______m1 = ______ 36. m1= ______m2 = _____ m5 = ______ Write an algebraic equation for each triangle and solve for x. 37. 38. 39. Equation: Equation: Equation: x = _______ 40. x = _______ 41. x = _______ 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. Centroid 66. A segment from a vertex that bisects the corner angle _____ D. Median 67. Cuts a segment in half and makes a 90 angle _____ E. Perpendicular 68. Point where medians intersect ______ Bisector BD is a MEDIAN of ∆ABC. Find each length. 69. 70. 71. AD = _______ AC = _______ AD = _______ DC = _______ AD = _______ AC = _______ 72. The medians on this picture are segments: ____________________________ 73. R is the centroid of ∆ABC and 74. A is the centroid of ∆LMN and AD = 9. 75. Q is the centroid of ∆CDE and AM = 40. QE = 14. D Equation: x = ______ RD =______ Equation: Equation: AR = ______ x = ______ AB =______ Draw and label the MEDIAN from vertex X. 76. BM = ______ x = ______ QF =______ 77. EF = ______ . x Fill in the blank. 78. 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. 79. 80. 81. Equation: Equation: Equation: x = _____ x = _____ PS = _____ RS = _____ x = _____ PM = _____ MN = _____ 82. 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. 83. 84. 85. Equation: x = _____ BC = _____ Equation: Equation: x = _____ AB = _____ DC = _____ x = _____ AD = _____ CB = _____ CD = _____ Write an equation and solve for x. 86. XY is the angle bisector of X. 87. PS is a median. 88. Equation: Equation: Equation to solve for x: Equation to solve for y: x = _____ x = _____ x = _____ y= _____ 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 89. 91. 90. 92. Find mJ first. __________________ __________________ __________________ __________________ 93. 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! 94. 1 cm, 2 cm, 3 cm _____________________ yes or no 95. 2 mm, 3 mm, 4 mm____________________ yes or no 96. 8 cm, 8 cm, 8 cm _____________________ yes or no 97. 9 mm, 9 mm, 18 mm ___________________ yes or no 98. 21 m, 4 m, 13 m______________________ yes or 100. Draw and label the ANGLE BISECTOR of X. 99. 50 cm, 50 cm, 25 cm___________________ no 102. X 101. Draw and label the PERPENDICULAR BISECTOR of 41. 103. 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 4. Mark each pair of corresponding angles Pairs of Corresponding Angles CD ________ C ______ XZ ________ X _______ EC ________ D ______ YX ________ Y _______ ZY ________ Z _______ ZXY _______ E ______ DE ________ ECD _______ Congruence Statement: Congruence Statement: and correspondingsides the congruent PQRtoshow ABC parts. 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 _____ mB = _____ mF = _____ mA = _____ Hint: How many degrees are in a triangle? DE _____ BC _____ DF _____ mA = _____ mF = _____ mB = _____ Mark the triangles to correspond to each postulate: 9. SSS 10. SAS 11. ASA EF _____ ED _____ CA _____ mD = _____ mF = _____ mE = _____ 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 and Postulate __________ ; AC MO 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__________________ LITTLE, BIG OR BOTH? 38. Draw AND LABEL the pair of little triangles. 39. Draw AND LABEL the pair of BIG triangles. Name the little triangles: Name the BIG triangles: Do the following corresponding parts belong to the little triangles, BIG triangles, or both? 40. 1 2 _____________41. 3 4 _____________42. A D _____________43. ABC DCB ____________ 44. BD CA ____________ 45. BE CE ____________ 46. BA CD ____________ 47. AE DE ____________ Is the segment a LEG or the HYPOTENUSE ? Name the ANGLE that is included between the two sides. 48. 51. CD and BC ________________ 52. AB and CB _______________ 53. DC and BD ________________ 49. 50. FE _____________ FD _____________ DE _____________ 54. 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 mC ______ mB ______ m1 ______ m2 _____ XO______ XZ _____ BC = ______ DC = ______ m3 ______ m4 _____ OY ______ WY _____ For each RHOMBUS, find each length or measure. 22. 23. 24. mC ______ mB ______ m1 ______ m2 _____ m1 ______ m2 _____ BC = ______ DC = ______ m3 ______ m4 _____ m 3 ______ m4 _____ For each RECTANGLE, find each length or measure. 25. 26. 27. m1 ______ m2 ______ m1 ______ m2 _____ XO_____ XZ _____ OY _____ BC = ______ DC = ______ m3 ______ m4 _____ WY _____ m1 ____ m2 ____ For each SQUARE, find each length or measure. 28. 29. 30. m1 ______ m2 ______ m1 ______ m2 _____ m1 ______ m2 _____ BC = ______ DC = ______ m3 ______ m4 _____ m3 ______ m4 _____ m2 _____ For each TRAPEZOID, find each length or angle measure 31. 32. mR ______ mT ______ 33. mP _____ mS ____ m1 ______ mA _____ PA _____ m3 _____ m4 ______ 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 = _______ mABC = ______ mBCD = ______ 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. m1= ______ mD= ______ mD= ______ m1= ______