Name:__________________________________ Hr: ______ Geometry – Semester Exam Review GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. Go through your folders and find all of the quiz and test reviews that we have been doing all semester. Use them to help you with each chapter. 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. I will be checking your review packet along the way so make sure you are keeping up with the work! Midterm Review Assignments Date Assignment
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Geometry 2-B · Web viewGeometry – Semester Exam Review. GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. Go through
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GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. Go through your folders and find all of the quiz and test reviews that we have been doing all semester. Use them to help you with each chapter.
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.
I will be checking your review packet along the way so make sure you are keeping up with the work!
Midterm Review Assignments
1st Hour Exam: Tuesday, January 26th 8:00 – 9:30 3rd Hour Exam: Friday, January 29th 8: 00 – 9:30
Date Assignment
Geometry - Ch. 1 Review Name: _________________________MATCHING...Answers will be used more than once.
1. _______ Like a dot. Indicates a location.
2. _______ Flat, goes forever in all directions.
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.
6. _______ Two points determine a _______.
7. _______ Three non-collinear points determine a _-__. 8. _______ Points on the same line are ____.
9. _______ Points on the same plane are ____.
10. _______ Two lines intersect in a ____.
11. _______ Two planes intersect in a ____.
12. _______ Two lines that never intersect are ______.
13. _______ Segments with the same length are ____.
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
17. _______ Angle that measures less than 90
18. _______ Angle that is more than 90 but less than
180
19. _______ Angle that measures exactly 180
20. _______ Unit of measure to measure angles
21. _______ Instrument used to measure angles
22. _______ The sides of an angle are called ______.
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. A⃗N and M⃗A _____40. M⃗A and A⃗M _____ 41. N⃗A and N⃗M _____
Use the diagram to name the intersection of each pair of lines.
42. D⃗B and E⃗F _____43. F⃗G and C⃗D _____ 44. E⃗D and C⃗F _____ 45. B⃗F and E⃗D ______ *
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.
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°._____________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. ____________
11. Draw the midpoint of AB and label it X, then name the resulting congruent segments.
The congruent segments are:__________A segment has _____ midpoint(s).
12. M is the midpoint of JK . Write an equation, solve for x, and find the indicated lengths.
x= _______ JM= _________ MK=________
13. Use the Midpoint Formula to find the coordinate of the midpoint.(-7, 5) and (5, 3)
Midpoint: ( , )
14. Draw and label three bisectors of this segment.
A segment has _____ bisectors
15. Notice the bisector and corresponding tick marks. Find the indicated lengths.
CB= _________ AB=__________
16. Notice the bisector and corresponding tick marks. Find the indicated lengths. AC = 150 yards
AB= ___________ BC=___________17.
Name the bisector of this angle. _______Name the congruent angles: ________
18. B⃗D bisects ∠ABC
m∠1 = 56°m∠2=_________m∠ABC= _________
19. Y⃗A bisects ∠XYZ
m∠XYZ = 56°m∠1=_________m∠2= _________
20. Given that B⃗D is the bisector of ∠ABC, write an ALGEBRAIC EQUATION and solve.
Y=______m∠ABD=_______ m∠ABC=_____
21. Given that W⃗Z is the bisector of ∠XWY, write an ALGEBRAIC EQUATION and solve.
x=______m∠XWZ=_______ m∠ZWY=_____
22. Name the adjacent angles in this picture.
Adjacent angles:_________
23. 15°Complement:Supplement:
24. 172°Complement:Supplement:
25.
These angles add up to ______ m∠1=_____
26.
These angles add up to ______ m∠1=_____27.
These angles are ____________ m∠1=_____
28.
m∠1=_______ m∠2=_______ m∠3=______
29.
m∠1=_______ m∠2=_______
m∠3=_______ m∠4=_______
Terms:Complementary
AnglesSupplementary Angles
MidpointAdjacent Angles
Segment BisectorAngle Bisector
Linear PairVertical Angles
Inductive ReasoningDeductive Reasoning
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 _____Equation:
x= _____ m∠ABD=______ m∠DBC=______
33. These angles add are_____Equation:
x = _______
34. These angles add up to _____Equation:
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 pattern41. -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 Write a single if-then statement that follows from the Statements below? pair of true statements below.44. If you wash your cotton t-shirt in hot water, 45. If the ball is thrown at a window,It will shrink. You wash your cotton t-shirt in hot water. it will hit the window. If the ball hits the
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 ______
15. ∠10 and ∠ 16 ____ 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. 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.
20. 21. 22. 23.
24. 25. JKLM is a parallelogram 26. 27.
1 _____ 2 _____ K _____ L _____ H _____ F _____ 1 _____ 2 _____
3 _____ 4 _____ M _____
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 ______
A. alternate interiorB. same-side interior C. alternate exterior D. same-side exteriorE. correspondingF. verticalG. linear pairl
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 Relationship: congruent or supplementary Relationship: congruent or supplementaryEquation: Equation: Equation:
x = ________ x = ________ x = ________
42. 43. 44.
Relationship: congruent or supplementary Relationship: congruent or supplementary Relationship: complementary or supplementaryEquation: Equation: 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. 49. 50.
Circle the segments or lines that must be parallel.
Hint: There are 180 in a triangle!
132。
m n
40
40
51. 52. 53.
Choices: SW || MI or SM || WI Choices: IH || FG or FI || GH Choices: 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 toTZ . ____________________________
59. Name four segments that intersect TZ . __________________________
60. Name four segments skew toTZ . _______________________________
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.
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!)
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
Geometry Chapter 4 Review Name:__________________________________________MATCH each type of triangle with its definition. Equilateral Triangle _____ Isosceles Triangle _____ Scalene Triangle _____
m5 = ______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: Equation:
y = ______ 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.
Equation: Equation: Equation:
x = ______ x = ______ x = ______
46. 47. 48.
Equation: Equation: Equation:
x≈ ________ x≈ ________ x≈ ________
x x x
x33
x
x 17
13
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?
Equation:
50. A 26-ft wire is attached to an electrical pole. The wireattaches to a stake on the ground. If the stake is 10 feetfrom the base of the pole. How tall is the pole?
Equation:
51. Find the length of the diagonal of a square if each side 10 cm.
Equation:
52. Mary hikes 7 km north and 5 km west.How far is she from her starting point?
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= 63. ( -1, 2 ) and ( 3, 0 )√ ( x − x )2 + ( y − y )2
Matching:64. A segment from a vertex to the midpoint of the opposite side _____
65. A segment from a vertex perpendicular to the opposite side _____
66. A segment from a vertex that bisects the corner angle _____
67. Cuts a segment in half and makes a 90 angle _____
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. .
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. 81.
Equation: Equation: Equation:
x = _____ BC = _____ DC = _____ x = _____ AB = _____ CB = _____ x = _____ AD = _____ CD = _____ Write an equation and solve for x.
A. AltitudeB. Angle BisectorC. MedianD. Perpendicular Bisector
x
41.
82. 83.
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 longest84. 85. 86. 87.
__________________ __________________ __________________ __________________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 no 94. 50 cm, 50 cm, 25 cm___________________ yes or no
95. Draw and label theANGLE BISECTOR of X.
96. Draw and label thePERPENDICULAR BISECTOR
of AB .
XY is the angle bisector of X. PS is a median.
Find mJ first.
97.
98.X
BA
Hint: How many degrees are in a triangle?
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 ≃ _______DE ≃ ________ ∠ E ≃ ______ ZY ≃ ________ ∠ Z ≃ _______Congruence Statement: Δ ECD ≃ Δ _______ Congruence Statement: Δ ZXY ≃ Δ _______
5. CPCTC stands for: ___________________ Parts of ___________________ Triangles are _____________________.
Given Δ ABC ≃ Δ DEF , find the missing length or angle measure.
6. 7. 8.
DE = _____ BC = _____ AC = _____ DE = _____ BC = _____ DF = _____ EF = _____ ED = _____CA = _____mB = _____ mF = _____ mA = _____ mA = _____ mF = _____ mB = _____ mD = _____ mF = _____ mE = _____
Mark the triangles to correspond to each postulate:9. SSS 10. SAS 11. ASA 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.
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 32. BC ≃ YZ ;∠C ≃ ∠Z ASA Postulate
Pair of sides or angles needed__________________ Pair of sides or angles needed__________________ Pair of sides or angles needed__________________
33. BC ≃ EC ; SAS Postulate 34. AC ≃ XZ ASA Postulate 35. AC ≃ XZ SSS Postulate (Hint: Mark "free" angles!)
Pair of angles needed__________________ Pair of sides needed__________________
Pair of sides needed_____________ Pair of angles needed__________________ Pair of sides needed__________________
36. AB ≃ XY ; SAS Postulate (TWO solutions)(Hint: Mark given sides… each solution has a pair of sides and a pair of angles.)
ONE WAY: OR 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. FE _____________
39. FD _____________
40. 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
A. Opposite sides are congruentB. Opposite angles are congruentC. Consecutive angles are supplementaryD. Diagonals bisect each otherE. Diagonal bisect the corner anglesF. Diagonals are congruentG. Diagonals are perpendicular
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 ______________________________________
A
RhombusUsing the properties of each shape to write and solve an algebraic equation for each picture.
38. 39. 40.
Equation: Equation: Equation:
x = _______ mABC = ______ mBCD = ______ x = _______ x = _______
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 E. 7 sides46. Quadrilateral 47. Hexagon B. 4 sides F. 8 sides48. Nonagon 49. Pentagon C. 5 sides G. 9 sides50. Heptagon 51. Triangle D. 6 sides H. 10 sides
Classify (Name) the polygon by its number of sides.52. 53. 54. 55. 56. 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.