Download 1st Semester review Answers

1st Semester review Answers
Chapter 1
1. How many point do you need to form:
A line____2 points_______________
A plane __3 Noncollinear points________
6. Find the following given A (4, ─3) D ( 8, 1)
Slope of AD ______1______
Length of AD
4 2 _____________
Midpoint of AD __(6, −1)______________
Space 4 noncollinear, noncoplanar points
Use the addition postulates to find the following
2. If B is between A and C AB = 5x BC = 2x + 3
AC = 45
Find AB. ______x = 6 AB = 30_____
7. Find the following given B (─2, 7) C (4, 5)
Slope of BC ______−
1
_________________
3
Length of BC _____ 2 10 _________________
3. X ix in the interior of <ABC and m<ABC = 78
m<ABX = 33
Midpoint of BC _ (1, 6)__________
Find m<XBC___45_____
8. Find x
x = 11
10x+25=13x-8
4. Define the following and sketch a picture:
10x + 25
Acute angle__< 90°____________________
13x ─ 8
Right angle ____= 90 °__________
Obtuse angle ___> 90 °____________________
Straight angle _______= 180 °_________
9.
9x+20+4x-9=180
x = 13
9x + 20
4x ─ 9
Vertical angles ___________________________
Linear Pair angles _________________________
If AB = 14 find BD = 14____
10. Find the complement and supplement of angles
Angle of 62.5º
Complement ____27.5°_____
If BD = 16 find AD = __32____
Supplement____117.5°________
If BD = 2x + 4 & AB = 3x ─ 1 find
Angle of 2x + 40
Complement ___90-(2x+40)= 50 − 2x°______
5. If B is the midpoint of AD find the following
AD = _28____
Supplement _180-(2x+40)= ___140 − 2x °_____
Chapter 2
11. Identify the hypothesis and conclusion,
If a number is a perfect square, then it is positive.
Hypothesis __ a number is a perfect square
Chapter 3
17. Identify the type of angles
3 4
2 1
Conclusion_______ it is positive _________
Is it true or false?____True _______
Write the converse of the conditional above.
Is it T or F?
If a number is positive, then it is a
perfect square.
False 6
7
6
8
5
<3 & <7 ____Corresponding angles____
<4 & <6 ___Alternate Exterior angles_
12. What is the next number in the pattern?
<2 & <8 ___ Alternate Interior angles ___
1, 10, 18, 25, _31____
<1 & <8 _Same Side Interior or Consecutive
Interior angles
13. Given If p →q, write the
Converse_______ q →p __
Inverse____~ p → ~q __________
Contrapositive____~ q → ~p ____
List the 2 logically equivalent pairs.
Converse & Inverse
Conditional & Contrapositive
14. What is a counterexample?_
AN EXAMPLE THAT PROVES THAT A
CONJECTURE IS FALSE. Satisfies the hyp
but fails the conclusion
Identify the following (15 & 16) as either the
Law of Syllogism or the Law of Detachment
15.Given: If the front goes thru, then it will rain.
If it rains, then it will flood.
Conjecture: If the front goes thru, then it will flood.
___Law of Syllogism____________
16. Given: If 2 segments are  , then they are =.
AD  BC .
Conjecture: AD = BC .
_Law of Detactment____________
Given the lines ║
18. Given m<1 = 4x + 8 m<5 = 6x ─2
Find x __x = 5_________
19. Given: m<2 = 11x ─ 5 m<7 = 6x + 15
Find m<7 ___x = 10 m<7 = 75_______
20. Given m<7 = 7x + 15 m<1 = 9x + 3
Find m<1_ x = 6 m<1 = 57_________
Write the equation of the following lines:
21. in y-intercept form a line parallel to y = 5x + 3
passing through (─2, 7)
________y = 5x + 17______________
Determine if the pair of lines are parallel, intersect,
or coincide.
22. 3x = ─6y + 3
23. 4x ─ 3y = ─ 1
2y = ─x + 1
3x ─ y = ─2
Coincident
intersecting (−1,−1)
Same slope/same y int
Use slope to determine whether the lines are parallel,
perpendicular, or neither.
24. AB & CD A(2, 6) B(8, 3) C(1, 4) D(7, 1)
Slopes −½ Same slope parallel
25. AB & CD A( ─3, 4) B(5, 2) C(6, 6) D( 4, ─2)
Slopes 4 & −¼ Negative reciprocals
Perpendicular
HL
31.
26. Define the following:
Skew__Noncoplanar lines that do not
intersect
Parallel _coplanar lines that do not intersect_
Perpendicular_2 lines that form a 90°angle_
L
Chapter 4
J
27. If ABC  XYZ name the 6 pairs of corresponding
parts.
Angles <A  <X ; <B  <Y ; <C  <Z
Sides AB  XY ; BC  YZ ; AC  XZ
28. Classify
ABD and BCD
K
B
A
C
ASA
32.
D
E
25º
60º
A
70º
A
B
||
C
||
D
C
ABD acute
BCD obtuse
29. Solve for x and find the angle measurements.
B
L
(
(3x ─ 5)º
SAS
33.
(2x + 15)º
R
120º
K
M
N
x = 22 m<K = 59 m<L = 61
S
||
T
||
U
AAS or HL
34.
R
Why are the following triangles congruent?
30.
SAS
C
B
S
D
A
T
U
Chapter 5
Name the special line segments and the point of
concurrency for each of the following:
Given X,Y, Z are midpoints
A
15
Z
C
12
35.
36.
18
X
Altitude
Angle Bisector
Orthocenter
Incenter
B
15_
46.Find XY
37.
38.
Y
47.Find BC 36__
Perpendicular Bisector
Median
Circumcenter
Centroid
48.Find the perimeter of triangle XYZ 45_
49.Find AB __24__
Given 3 lengths, state if they can make a triangle.
39. 3, 6, 10
No
40. 5, 8, 4
yes
41. 19, 6, 14
yes
M is the centroid. Find the following
B
42. Find the range for the 3rd side given two sides of 10
and 8.
2<x<18
43. m<ABC > m<DBC
D
M
A
B
12
E
F
12
50. CM = 28 find MD = 14__
10
A
C
D
8
V
S
52. MB = 18 find BF = 27____
31
28
44. ST < UV
51. AE = 36 find MA = 24___
U
Right Triangles
T
Classify the following triangles
53. 4, 7, 9 obtuse 92_____42 + 72
54. 5, 12, 13 right
45. List the sides in order from least to greatest.
I
48º
J
56. Find the geometric mean of 4 & 10 ± 2 10
62º
K
55. 4, 6, 7 acute
sides JK ; IJ ; IK
C
x
57.
x
Proofs
64. Given: P is the midpoint of
Prove:
3
6
x = 3 5 Pythagorean Thm
T
8
58.
and
.
R
P
x
30
S
3033
y
0
x=4 y= 4 3
1) P is midpt of TQ & RS
2)
45
59. x
Q
TP  PQ; RP  PS
1) Given
2) Def of Midpoint [1]
3) <TPR and <SPQ are vert < 3) Def vertical <s
4. <TPR  <SPQ
4) vertical angles are  [2]
5)
5) SAS [2,3]
10
y
x= 5 2
y = 5 2
65. Given: T is the midpoint of
Prove: TPR  TPS
60.
. TP  SR
P
y
9
60
S
x
x=
3 3
61.
y =6 3
5
1) T is the midpoint of
62.
8
Pythyagorean Thm
x
45 Isos
x= 8 2
y
63.
1) Given
2) Def of Midpt [1]
3) m<STP = 90 m< RTP=90 3) Def of perpendicular[1]
4) m<STP = m< RTP
4) substitution [3]
5) STP  RTP
5) Def of  [4]
15
15
R
TP  SR
2) RT  TS
x
x = 10 2
T
x = 7.5
y = 7.5 3
6)
7)
PT  PT
TPR  TPS
6) Reflexive
7) SAS [2,5,6]
66. Given: BC ║ EF
Prove: <1 and <4 are supplementary
B
4
2
E
C
3
1
F
1) BC ║ EF
1) Given
2) <2 and <4 are SSI 2) Def SSI
3)<2 & <4 are suppl
3) If lines parallel, then
SSI<’s suppl [1]
4)m<2+m<4=180
4) Def of suppl [2]
4.5) <1 &<2 vert <
4.5)Def vert <
5) 1  2
5) vertical angles congruent[dia]
6) m<1=m<2
6) Def of congruence [4]
7)m<1+m<4=180
7) substitution [3,5]
8) <1 & <4 are suppl 8) Def of suppl [6]
67. Given: l ║ m; m<1 = m<2
Prove: m<2 = m<4
1 2
l
4
3
m
1) l ║ m; m<1 = m<2
2) <1 and <4 are corr <
3) 1  4
4) m<1=m<4
5) m<2=m<4
1) Given
2) Def corr <
3) If lines parallel, then
corr <’s  [1]
4) Def of congruence [2]
5) Substitution [1,3]