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. 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.

Midterm Review Assignments

Date Assignment Done!

Wednesday 1/11 Chapter 1

Thursday 1/12 Chapter 2

Friday 1/13 Chapter 3

Tuesday 1/17 Chapter 4

Wednesday 1/18 Chapter 5

Thursday 1/19 Chapter 6

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 ______.

A. Collinear

B. Coplanar

C. Line

D. Plane

E. Point

F. Ray(s)

G. Segment

H. Congruent

I. Parallel

J. Segment Addition

Postulate

K. Angle Addition

Postulate

L. Acute

M. Degree

N. Obtuse

O. Protractor

P. Right

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 ____________ 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? ____

.B

Use the Segment Addition Postulate to find each length. 55. 56. 57. NQ = ___________ GH= ___________ XZ = ___________ 58. 59. 60. RT = ___________ LM = ___________ FG = ___________ Use the Segment Addition Postulate to write an ALGEBRAIC EQUATION. Then, solve the equation for x.

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: ________________________ ________________________

Given the picture, state the measure of each angle or write the measure in the proper location on the diagram.

65.

PRTm _____ TRSm ____

66.

VEZm _____

REUm _____ VEUm _____

67.

10YXZm 50WXYm

60WXZm

68.

1101m 702m

1103m 704m

Find the measure of each angle using addition or subtraction.

69. m RSP = 20 m PST = 30 m RST = _______

70. m ABD = 120 mABC = 35 m CBD = _______

71. m TOS = 150 m TOR = _________ m SOR = _______

72. m EFH =15 m EFG = _________ m HFG = _______

73. m PQR = 23 m PQS = _____ m RQS= _______

74. m RQS = 57 m PQS = _____ m PQR = _______

J K

22

2x - 4

3x - 4

40

25

32

8x + 9 27

5x - 1

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. mKLM = _________ 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°._____________

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 ������ 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 �����. 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. �������� bisects ∠ABC

m∠1 = 56°

m∠2=_________

m∠ABC= _________

19. ������� bisects ∠XYZ

m∠XYZ = 56°

m∠1=_________

m∠2= _________

20. Given that �������� is the bisector of

∠ABC, write an ALGEBRAIC EQUATION

and solve.

Y=______m∠ABD=_______ m∠ABC=_____

21. Given that �������� 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

Angles Supplementary Angles

Midpoint Adjacent Angles Segment Bisector

Angle Bisector Linear Pair

Vertical Angles Inductive Reasoning

Deductive 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 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 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 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 ______

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 interior

B. same-side interior

C. alternate exterior

D. same-side exterior

E. corresponding

F. vertical

G. linear pair

r s

m

l

51

2 42

1

This is a trapezoid.

50 150 70 80 40

60

30 1

2

3 4

31. SONG is a parallelogram 32. 33.

1 ______ 2 ______ SGN ______ 1 ______ 2 ______ 1 ______ 2 ______ 3 ______ 4 ______ 3 ______ 4 ______ 5 _______ 3 ______ 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 Relationship: congruent or supplementary Relationship: congruent or supplementary Equation: Equation: Equation:

x = ________ x = ________ x = ________

42. 43. 44.

Relationship: congruent or supplementary Relationship: congruent or supplementary Relationship: complementary or supplementary Equation: 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.

Hint: There are 180 in a triangle!

132。

40

40

Circle the segments or lines that must be parallel. 51. 52. 53.

Choices: WISMorMISW |||| Choices: GHFIorFGIH |||| Choices: yxornm ||||

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 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.

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 75. lines m and n

Choices: CONGRUENT INTERSECT PARALLEL PLANE RIGHT RIGHT ANGLES

88。

88。 87

。

x

y

m n

J K

·Z

J K

·Z

Geometry Chapter 4 Review Name:__________________________________________

MATCH each type of triangle with its definition. Equilateral Triangle _____

Isosceles Triangle _____

Scalene Triangle _____

Equiangular Triangle _____

Acute Triangle _____

Right Triangle _____

Obtuse Triangle _____

A. Triangle with one right angle.

B. Triangle with all (3) equal sides.

C. Triangle with all (3) equal angles.

D. Triangle with three acute angles.

E. Triangle with one obtuse angle.

F. Triangle with two equal sides.

G. Triangle with no equal sides.

Classify the triangle by its sides.

1. 2. 3. 4. Classify the triangle by its angles. 5. 6. 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 Angles: acute obtuse equiangular rt.

Identify the side opposite each angle. Use the picture to name the following. Name the equal sides and equal angles in each picture.

13. 14. 15. 16.

Side opposite X: ________

Side opposite Y: ________ Legs______________ Base _______ Equal sides: _______________ Equal sides: _______________

Side opposite Z: ________ Vertex angle _______ Base angles ___________ Equal angles: ______________ Equal angles: ______________ *Use correct notation!

Using ABC, name the following. 17. The interior angles of this triangle are ____________________ 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. m3= _____

25. m1 = _____ m2 = _____ 26. m1 = _____ 27. m1= ____ 28. m1 = ____ m2= ______

m3= ______ m4= ______ m5= ______

x

x

29. x = _____ 30. x = _____ 31. m1 = _____ m2 = _____ 32. m1 = _____ m2 = ____

33. m8 = ______ m9 = ______ 34. m3 = ______ m4 = ______ 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 = _______ 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 33

x

x 17

13

22 yyxx

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 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:

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 )

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 = _____

A. Altitude

B. Angle Bisector

C. Median

D. Perpendicular

Bisector

x

41.

Write an equation and solve for x. 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 longest

84. 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 the ANGLE BISECTOR of X.

96. Draw and label the PERPENDICULAR BISECTOR

of .AB

XY is the angle bisector of X. PS is a median.

Find mJ first.

97.

98.

X

B A

ABCPQR

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: _______ECD Congruence Statement: _______ZXY

5. CPCTC stands for: ___________________ Parts of ___________________ Triangles are _____________________.

Given DEFABC , 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. 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

4. Mark each pair of corresponding angles

and corresponding sides to show the congruent parts.

Hint: How many degrees are in a triangle?

U

Mark the pictures first and then state what postulate proves the triangles congruent. Choices: SSS, SAS, ASA, AAS, H-L or none.

26. MNAB ; MA 27. MNAB ; MA 28. MNAB ; MOAC 29. MNAB ; NOBC

and NB and OC and NOBC and NB

Postulate __________ Postulate __________ Postulate __________ Postulate __________

Using the given information and method, state the PAIRS of additional information needed to prove the triangles congruent.

30. YZBC ; ZC AAS Postulate 31. YZBC ; ZC ; SAS Postulate 32. YZBC ; ZC ASA Postulate

Pair of sides or angles needed__________________ Pair of sides or angles needed__________________ Pair of sides or angles needed__________________

33. ECBC ; SAS Postulate 34. XZAC ASA Postulate 35. XZAC 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. XYAB ; 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. XYAB ; 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. BCandCD ________________

42. CBandAB _______________

43. BDandDC ________________

44. BDandAB ________________

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: _________________________________________

Picture:

Properties: 1. ______ 2. ______ 3. ______ 4. ______

CHOICES FOR PROPERTIES:

A. Opposite sides are congruent

B. Opposite angles are congruent

C. Consecutive angles are supplementary

D. Diagonals bisect each other

E. Diagonal bisect the corner angles

F. Diagonals are congruent

G. Diagonals are perpendicular

Rhombus

Definition: _________________________________________

Picture: Properties: 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. ______

Rectangle

Definition: _________________________________________

Picture:

Properties: 1. ______ 2. ______ 3. ______ 4. ______ 5. ______

Square

Definition: _________________________________________

Picture: Properties: 1. ______ 2. ______ 3. ______ 4. ______

5. ______ 6. ______ 7. ______

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 ______.

Study the Venn Diagram which relates all of these quadrilaterals..

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 _______ 8. The diagonals of a square are perpendicular _____________ 9. The diagonals of a rectangle are congruent ___________ 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.

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 _____

For each TRAPEZOID, find each length or angle measure 31. 32. 33.

mR ______ mT ______

mP _____ mS ____

m1 ______ m2 _____

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

Rhombus

Using 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 sides

46. Quadrilateral 47. Hexagon 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

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. m1= ______ m1= ______ mD= ______ mD= ______

Rectangle

Parallelogram

Square

Trapezoid

IsoscelesTrapezoid