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Geometry Midterm Study Guide
Name: _______________________
HW 42: 1-30 all
(Chapters 1-3)
HW 43: 31-60 all
(Chapters 4, 6-7, 8.1)
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HW #42: Problems 1 – 30 all
For question #1, justify each statement with a Geometry Rule
1.) a) HP = HP
b. HP + PT = HT
M
Z
T
c. mGPT + mTPR = 180
G
d. If P is the midpoint of GR, then GP = PR.
P
R
H
e. mHPG + mGPZ = mHPZ.
f. mHPG  mTPR
g. If GR  MP, then GPM and MPR are right angles
h. If GPZ and ZPM are complementary, then mGPZ + mZPM = 90
i. If PT bisects MPR, then mMPT = mTPR
j. HT bisects GR, then P is the midpoint of GR
k. If GPT and TPR are supplementary, then their sum is 180
For questions 2-5, complete the sentences:
2. The intersection of two distinct lines is a ________.
3. The intersection of two distinct planes is a _________.
4. The intersection of a plane and a line is a ____________.
5. An example of an undefined term is a______________ or a ____________ or a _____________.
For questions 6-9, write an equation and solve.
6. Solve for x, mXAB and mBAY ,
7. Solve for x, mABC, mDBE
AB bisects XAY
B
X
A
D
4x - 11
4x - 27
x + 40
A
Y
C
B
3 + 2x
E
8. Solve for x, mFGH, mHGI
9. AB = x + 1, BC = 2x + 4, AC = 10x –16.
Solve for x, AB, BC, and AC
Solve for x, AB, BC, a
H
A
8x - 40
F
B
C
2x + 20
I
G
10. For the given points A and B, find AB (the length of AB ) and the midpoint of AB : A(6, -3) and (2, -8)
(a) AB =
(b) midpoint =
For #11, two pairs of parallel lines are shown. Identify whether the pair of angles are vertical angles,
same side interior angles, corresponding angles, alternate interior angles, same-side exterior angles, or
alternate exterior angles. Then, name their relationship (e.g. congruent, supplementary, etc.)
11.) a) 2 and 6 b.) 1 and 6
3
7
4
c.) 5 and 2
2
d.) 1 and 3
5
1
6
In the diagrams, the lines shown are parallel. Write an equation and solve for x and y. Justify your work.
Find the values of x and y.
12.)
13.)
40
5y
y
20
15x-20
x
5x
For #14, use the given information to name the segments that must be parallel. If there are no such
segments, write none. For #15, use the given information to complete the blanks about angles formed by
parallel lines.
A
B
14.) a) 3  10 15.) a) AE BD
2
1
3
7   ___
b) 7  10
10
F
9
11 8
b.) FB EC
7
E
m7  m8  m ____  180
5
4 C
6
D
16.) Prove the converse of the alt ext angles theorem:
1
If two lines and a transversal form alternate exterior angles that
are congruent, then the two lines are parallel.
Given: 1  3
Prove: m n
Statements
2
3
Reasons
1.)
1.)
2.)
2.)
3.)
3.)
4.)
4.)
17.) Fill in the blanks with a numerical answer:
a.) the sum of the interior angles of a triangle is _____
b) each angle of an equilateral triangle measures _____
c) acute triangles have ______ acute angles
d) obtuse triangles have _____ obtuse angle(s) and _____ acute angles
e) right triangles have _____ right angle(s)
f) isosceles triangles have _____ congruent sides
g) scalene triangles have _____ congruent sides
18.) classify the triangle based on angles and sides (Hint: find x first)
23.)
8x - 20
3x + 5
2x
For #19, use the diagram for reference. Show all equations and work.
a.)
If m6  42 and m8  61,
then m10  ____
11
6
9
If m6  7 x, m7  2 x  5,
b) and m11  6 x + 35, then
x = ___.
8
7
10
For #20-22, find the requested information about regular polygons.
20.) A regular polygon has 5
21.) A regular polygon has an 22.) A regular polygon has an
sides. Find:
interior angle of 140 . Find
exterior angle of 10 . Find:
a) sum of exterior angles
a) each exterior angle
a) each interior angle
b) each exterior angle
b) sum of exterior angles
b) sum of exterior angles
c) each interior angle
c) number of sides
c) number of sides
d) sum of interior angles
d) sum of interior angles
d) sum of interior angles
For #23, graph the lines using the requested information.
23.) a.) Graph each line using the slope and yb.) Graph the lines using the x and y intercepts:
intercept:
3x – 2y = 8
2x + 3y = 6
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
3
4
2
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
1
9 10
-2
-3
-4
-5
-6
-7
-8
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9 10
-2
-3
-4
-5
-6
-9
-7
-10
-8
-9
-10
For #24-27, write the equation of the line:
24. through (1, -2) with slope -3 in slopeintercept form
25. through (6, 2) and parallel to x – 2y = 5 in
slope-intercept form
26. Through (2, -1) and perpendicular to
x + 3y = 7 in standard form
27. through (3, 2) and (4, 7) in slope-intercept
form
For #28, write an equation and solve for the angles.
28. The sum of an angle’s complement and twice its supplement is 324°. Find the angle, its complement, and
its supplement. (hint: let x = angle, 90 – x = complement, 180 – x = supplement)
For #29 give a one-word response that best describes the answer:
29.(a) the supplement of an acute angle is ______________
(b) the complement of an acute angle _____________
(c) the supplement of an obtuse angle is ______________
(d) the supplement of a right angle is ____________
30. The perimeter of ABC is 36. Is the
triangle equilateral, isosceles, or scalene?
B
3x + 1
2x + 2
A
4x - 3
C
**End of HW#42**
Homework #43 (Problems 31-60)
31. Given: WX ZY , XY WZ
X
Y
3
4
Prove: X  Z
2
W
1
Z
Statements
1. _________________________
2. _________________________
_________________________
3. _________________________
4. _________________________
5. _________________________
Reasons
1. ________________________
2. ________________________
________________________
3. ________________________
4. ________________________
5. ________________________
B
D
32. Given: AB DE , C is the midpoint of BE
Prove: AC  CD
C
A
Statements
1. _________________________
2. _________________________
3. _________________________
4. _________________________
5. _________________________
6. _________________________
33. ABC is equilateral. If mA  2 x  y and
mB  4 x  y , solve for x and y.
E
Reasons
1. ________________________
2. ________________________
3. ________________________
4. ________________________
5. ________________________
6. ________________________
34. Solve for x:
B
30
A
35. If SBF  TCG then:
a) FS  _______
2x + 17
64
58
6x - 7
C
36. List all the postulates that you can use to prove
that two triangles are congruent.
b) B  ______
c) CT  _______
37. Complete: ____  _____ by _______
E
38. Complete: ____  _____ by _______
X
G
Y
F
D
H
W
Z
WX YZ , WX  YZ
B
39. Given:
1 2
3
1
C
A
Prove: AB  CB
E
Statements
1.)
Reasons
1.)
2.)
2.)
3.)
3.)
4.)
4.)
40. Given:
ABC  DCB and A  D
D
2
A
D
Prove: AB  DC
B
Statements
1.)
Reasons
1.)
2.)
2.)
3.)
3.)
4.)
4.)
C
41. Write (A) the converse, (B) the inverse, and (C) the contrapositive of the statement and whether each is true
or false.
“If mA  50 , then  A is acute.”
A ______________________________________________________ T/F: _____
B ______________________________________________________ T/F: _____
C ______________________________________________________ T/F: _____
42.) Fill in the blanks: Opposite sides of a parallelogram are both (a)__________________ and
(b)___________________. Opposite angles of a parallelogram are (c) __________________ and consecutive
angles of a parallelogram are (d) ____________________. Diagonals of a parallelogram (e) __________
____________________.
43.) Write the letter of every special quadrilateral that has the given property.
A Parallelogram
B Rectangle
D Square
E Trapezoid
a. All sides congruent.
a. _________
C Rhombus
b. _________
c. _________
b. Diagonals bisect corner angles.
d. _________
c. Two pairs of sides are congruent.
d. Diagonals are congruent.
e. _________
e. Diagonals are perpendicular.
44. PQRS is a parallelogram.
Find a, b, x, and y
45. PQRS is a parallelogram.
Find a, b, x, and y
R
Q
y
80
R
Q
64
b
P
x
20
x
a
b
a
10
GRIP is a rectangle. Complete:
46. If m1  20 , then find m2, m3, and m4
7
y
32
S
5
20
P
S
G
R
4
S
P
2
1
3
I
47. If PS = 6x – 4 and GI = 28, then x = _____
ABCD is a rhombus. Complete:
48. If m1  20 , then find m2, m3, and m4
B
3 4
A
C
2
1
49. If m1  5x  3 and m3  3x  5 , solve for x.
D
Trapezoids and their medians are shown. Solve for x.
50.
3x + 2
2x + 4
2x + 1
f. _________
f. Exactly one pair of parallel sides.
Give coordinates for points D and S without using any new variables.
51. parallelogram
52. rhombus
y
y
D
(c + a, b)
(0, d)
D
O
S
O
x
(c, 0)
x
S
(c, 0)
53.)
B
Given: 1  4
Prove:
AB  BC
A
1
3
2
4
Reasons
Statements
1.)
1.)
2.)
2.)
3.)
3.) Substitution
4.)
4.)
54.)
D
B
Given:
C is the midpoint of AD and BE
Prove:
A   D
C
C
A
E
Statements
Reasons
1.)
1.)
2.)
2.) Definition of Midpoint
3.)
3.)
4.)
5.)
 _______   _______
4.)
5.)
55.) Complete each sentence with always, sometimes, or never
a) A square is ___________ a rectangle
b) A rectangle is ____________ a square
c) A parallelogram is _____________ a trapezoid
d) A quadrilateral is ___________ a trapezoid
56.) Find the value of x.
57.) Find the geometric mean between 4 and 18.
120 ft
x
15 ft
20 ft
58.) Find the values of x & y. (Hint: use three
similar right triangles)
59.) Solve for x.
8
C
12
y
6
24
x
A
2 D
x
B
60.) A painter leans a 34 ft ladder against a house. The base of the ladder is 30 feet from the house. How high
on the house does the ladder reach?
Midterm Schedule:
Tuesday 11/3
Period 1 8:15 – 10:15
Period 2 10:40 – 12:40
Wednesday 11/4
Period 3 8:15 – 10:15
Period 4 10:40 – 12:40
Please bring the following to class for your midterm:






HW #42-43 (this completed, corrected packet)
Test Analysis worksheet from class on Monday
Completed late homework with a signed pass
Bathroom passes
Extra credit points
Something quiet to do in case you finish your midterm
early.