Suffolk Geometry Midterm Review 2010-2011
(copy question and diagram…….use your notes!!!!)
This will be collected and taken for a grade once we have completed the review.
1. Which lines are //? Justify.
2.
2
a
1200
3
4
1
6
5
7
b
4. Give the symbolic form:
a) 𝒎∡𝟕 = 𝟑𝒙 + 𝟓
𝒎∡𝟔 = 𝒙
a) Conditional:
b) Contrapositive:
c) Converse:
d) Inverse:
e) Biconditional:
f) Conjunction:
g) Disjunction:
8
0
55
a
3. Use problem #2 to solve for x.
b
c
600
List the special angle pairs and
their relationship.
b) 𝒎∡𝟒 = 𝟕𝒙 − 𝟏
𝒎∡𝟓 = 𝒙 + 𝟕
h) Law of detachment:
d
1000
i) Law of syllogism:
j) Law of contrapositive:
5. How do you determine if a
triangle is scalene, isosceles or
equilateral?
6. How do you determine if a
triangle is right, obtuse or
acute?
7. What determines if lines are
//?
8. What special angle pairs
do not determine // lines?
9. How do you prove triangles
≅?
10. U is between F and N.
UF = 4x, FN = 14x + 2, UN = 28-3x
Find the length of the longest
segment.
11. If you are given two sides of
a triangle, how do you
determine the length of the
third side?
12.
b) How do you prove ~ ?
14. Use # 13: If T is the
midpoint of AZ, find the
coordinates of Z.
15.
16.
8 1
b) Length TA =
𝒄) 𝑴𝑻𝑨 =
𝒆) 𝒎// =
4
t
a
3 6
7 2
𝒅) 𝒎𝑨𝑻 =
5
b
Name an angle pair and the
relationship to ensure a//b
𝒇) 𝒎⊥ =
N
R
200 500 250
T
O
A
M
L
A
T
E
Which lines are parallel?
O
b) U is the midpoint of FN.
UF = 4x and UN = 28-3x. How
long is FN?
13. A (-5,-2), T (1, -4)
a) AT =
D
O
S
500
p
Would these angles ensure p//t?
17. ∆𝑨𝑩𝑪 ≅ ∆______ Justify.
A
B
C
D
A
21. Draw and label ∆𝑨𝑩𝑪 where
̅̅̅̅ is the hypotenuse.
𝑨𝑪
18. ∆𝑨𝑩𝑪 ≅ ∆______ Justify.
A
C
B
D
A
22. Using diagram # 17,
AB = 5 and AC = 13, find BC.
19. ∆𝑨𝑩𝑪 ≅ ∆______ Justify.
A
C
B
20. ∆𝑨𝑩𝑪 ≅ ∆______ Justify.
A
D
B
E
B
23. List all the proportions if
YU//WH:
W
2
Y
2
U
2
H
2
D
24. List all the proportions if
∡𝑺𝑻𝑶 ≅ ∡𝑺𝑼𝑵, and
∡𝑺𝑶𝑻 ≅ ∡𝑺𝑵𝑼:
N
2
O
2
C
O
2
T
2
S
2
U
2
26. Is ∆𝑷𝑬𝑻~∆𝑯𝑼𝑮?
25. Use the diagram #23,
YU = 3, WH = 7, YO = 6,
HO = ______
U
2
P
U
4
2
U
2
29. Would 9.8, 5.1 and 4.7 form
a triangle?
5
1.6
1.8
U T
2
27
H
G
E 2
2 7.5
2
2
2
30. Given: ̅̅̅̅
𝑨𝑪 ≅ ̅̅̅̅
𝑪𝑭, ̅̅̅̅
𝑪𝑫 ≅ ̅̅̅̅
𝑪𝑩
What method would prove:
∆𝑪𝑨𝑫 ≅ ∆𝑪𝑭𝑩
A
B
33. Use the coordinates from
question # 13 to form ∆𝑪𝑨𝑻 ,
where C is located at the origin.
Graph ∆𝑪𝑨𝑻
37. Given: The sum of the
exterior angles of any polygon is
𝟑𝟔𝟎𝒐 . The exterior angle sum is
𝟑𝟔𝟎𝒐 . What statement follows
from the Law of Detachment?
E
F
C
D
34. Use question #29 to
determine which statement is
true.
a) 𝒎∡𝑪 is the least of three
angles.
b) 𝒎∡𝑪 is the greatest of three
angles.
c) 𝒎∡𝑻 is the least of three
angles.
d) 𝒎∡𝑻 is the greatest of three
angles.
38. If the slopes are negative
reciprocals then the lines are
perpendicular. If the lines are
perpendicular, then the slopes
are negative reciprocals. Write
a biconditional statement.
27. Using #23,
∡𝒀 = 𝟖𝟑𝒐, , ∡𝑼 = 𝟒𝟐𝒐, , list the
sides from longest to shortest.
28. Using #23, WO = 71.3cm,
WH = 70.2cm and HO = 68cm.
From smallest to largest, name
the angles of ∆𝑾𝑯𝑶.
31. Given ∆𝑳𝑼𝑽, determine
which statements are true or
false?
a) 𝒎∡𝑳 + 𝒎∡𝑼 = 𝟗𝟎𝒐
b) 𝒎∡𝑳 + 𝒎∡𝑼 < 𝟗𝟎𝒐
c) LU +UV > LV
d) LU + UV < LV
32. On a map VB, Suffolk and
Chesapeake form a triangle.
Suffolk to VB is 45 miles,
Chesapeake to VB is 31 miles.
What is a possible distance
between Chesapeake to Suffolk?
35. Using #29, find 𝒎𝑻𝑪
36. Draw and label pentagon
GRADE. Label each interior
angle 𝟏𝟐𝟓𝒐 , 𝟏𝟏𝟕𝒐 , 𝟓𝟎𝒐 ,
𝟏𝟎𝟎𝒐 𝒂𝒏𝒅 𝟏𝟒𝟖𝒐
respectively.
now find each adjacent exterior
angle.
a) Find 𝒎𝑻𝑨
b) Is 𝑻𝑨 ⊥ 𝑻𝑪? Justify.
39. Use #37 Write the following
statements:
a) Conditional:
40. Given: 𝒎∡𝑻 = 𝟒𝒙 + 𝟖,
𝒎∡𝑷 = 𝒙 + 𝟏
a) ∡𝑻 𝒂𝒏𝒅 ∡𝑷 are complements
Find the 𝒎∡𝑻
b) Converse:
c) Inverse:
b) ∡𝑻 𝒂𝒏𝒅 ∡𝑷 are supplements.
Find the 𝒎∡𝑷
d) Contrapositive:
45. Determine if MY⊥ 𝑷𝑰
41.
431 Cell Phone Subscribers
43.
Rectangles
M
Squares
AT&T 200
Verizon 195
P
Z
(8𝑥 + 20)𝑜
(3𝑥 + 5)𝑜
(9𝑥)𝑜
a) (All, None or Some)
subscribers belong to AT&T and
Verizon.
⃗⃗⃗⃗⃗⃗ 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 ∡𝑭𝑨𝑻
44. Given: 𝑨𝑵
𝒎∡𝑭𝑨𝑻 = 𝟖𝟐𝟎 ,
𝒎∡𝑭𝑨𝑵 = (𝟒𝒙 + 𝟐𝟓)𝟎 .
Find 𝒙.
I
Which statement is true?
a) All squares are rectangles.
b) All rectangles are squares.
c) Some rectangles are squares.
d) No square is a rectangle.
Y
b) How many persons subscribe
to AT&T and Verizon?
45. Given: YU//WH
Statements:
Reasons:
Prove: ∆𝒀𝑶𝑼~∆𝑯𝑶𝑾
1. YU//WH
___________
2. ∡𝑼𝒀𝑶 ≅ ∡𝑾𝑯𝑶 ___________
W
2
Y
2
∡𝑨 ≅ ∡𝑫
Prove: ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑪𝑩
3. ∡𝒀𝑶𝑼 ≅ ∡𝑯𝑶𝑾 ___________
O
2
U
2
46. Given: AB//DC
4. ∆𝒀𝑶𝑼~∆𝑯𝑶𝑾
A
___________
C
H
2
B
D
A
Statements:
Reasons:
1. AB//DC
----------------------
2. ∡𝑨𝑩𝑪 ≅ ∡𝑫𝑪𝑩
----------------------
3. ∡𝑨 ≅ ∡𝑫
----------------------
4. CB≅ 𝑪𝑩
5. ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑪𝑩
6. 𝑨𝑪 ≅ ∡𝑫𝑩
------------------------------------------_____________