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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 
m3  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
mABC = 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. mKLM = _________
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. 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 = _____
30.
33. m8 = ______ m9 = ______ 34.
x = _____
31. m1 = _____ m2 = _____
m3 = ______ m4 = ______
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 = _______
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 mJ 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
correspondingsides
the congruent
PQRtoshow
 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  _____
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
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
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= ______