Download 1st Semester Exam Review Chapter 1: Vocabulary Plane Postulate

1st Semester Exam Review
Chapter 1:
Vocabulary
Plane
Angle Bisector
Segment Bisector
Segment
Opposite Rays
Line
Postulate
Midpoint
Congruent Segments
Supplementary Angles
Congruent
Acute Angle
Linear pair of angles
Vertical Angles
Adjacent Angles
Coplanar
Hypotenuse
Right Angle
Vertex
Obtuse Angle
Collinear
Complementary Angles
Problems
Match each type of angle to its diagram.
________
1. Straight
________
2. Obtuse
________
3. Right
________
4. Acute
a.
b.
c.
Find each length.
5.
7.
AB =
BD =
6.
8.
AD =
A
B C D
–5
–2 0 2
BC =
9. Find AB given B is between A and C.
10. Find m ABC given m ABD = 78  .
11. Solve for x. M is the midpoint.
12.
BC
is a bisector for
ABD .
Solve for x if
mABD =  5x  4   and
mABC  2x  5  
=
.
13. M is the midpoint of LN . L has coordinates (–3, –1),
and M has coordinates (0, 1). Find the coordinates
of N.
15. Find the midpoint of  4,3 &  2,  7 .
14. Find the length of AB, with coordinates A(1, –2)
and B(–4, –4)
16. Find the distance between (–4, 3) & (–2, –7).
Leave your answer in radical form.
17. An angle measures 3 times its supplement. Find the 18. E is the midpoint of
measure of the angle and its supplement.
Use the diagram to name each of the following:
19. A plane _________
X
C●
D●
●
●A
20. A line ___________
B
B
DF , DE = 2x + 4, and
EF = 3x – 1. Find DE, EF, and DF.
Use the diagram to name each of the following:
24. Name a pair of
vertical angles
______________
25. Name a linear pair
21. Opposite rays
______ ______
22. 3 collinear points
_____ _____ _____
______________
26. Name a pair of adjacent angles
___________________
27. Name a pair of complementary angles
23. A segment containing point A ________
____________________
Chapter 2:
Vocabulary
Inductive Reasoning
Hypothesis
Converse
Biconditional Statement
Conjecture
Conclusion
Inverse
Polygon
Counterexample
Truth Value
Contrapositive
Triangle
Conditional Statement
Negation
Deductive Reasoning
Quadrilateral
Problems
Make a conjecture about the each pattern. Write the next two items.
1.
__________________________
2.
___________
___________
1 1 1 1
, , , ,...
3 6 12 24
______________________________
________ ________
Complete the conjecture.
3. The sum of an even number and an odd number is _______________.
4. A product of an integer and its reciprocal is _______________.
Determine whether the conjecture is true or false. If it is false, give a counterexample.
5. An even number plus 3 is always odd.
6. A prime number plus 3 is always even.
True……False
True……False
7. For any three points in a plane, there are three different lines that contain two of the points.
True……False
Determine if the conditional statement is true. If it is false give a counterexample.
8. If two angles are obtuse, then they are
9. If a pair of angles form a linear pair, then they
supplementary.
are supplementary.
True……False
True……False
10. If two angles are adjacent, then they have a common ray.
True……False
Given the conditional statement “If the measure of  1 is 105, then  1 is obtuse,” write the converse,
inverse and contrapositive, find the truth value of each.
11. converse: ______________________________________________________________ T……F
12. inverse: _______________________________________________________________ T……F
13. contrapositive: __________________________________________________________ T……F
14. Write a conditional statement from the sentence: “A rectangle has congruent diagonals.”
___________________________________________________________________________
15. Write the converse and a biconditional statement for the conditional:
“If a number is divisible by 10, then it ends in 0.”
converse: _____________________________________________________________________
biconditional: __________________________________________________________________
16. Determine if the biconditional “The sides of a triangle measure 3, 7, and 15 if and only if the
perimeter is 25 in.” is true. If false, give a counter example.
______________ ___________________________________________________________
17. Write the definition as a biconditional. “Parallel lines are coplanar lines that never intersect.”
___________________________________________________________________________
18. Identify the hypothesis and conclusion of the conditional statement. Underline the hypothesis once and
the conclusion twice.
“Two angles are supplementary angles if the sum of their measures is 180.
19. Write a conditional statement from the following.
“Sixteen-year-olds are eligible to drive.”
20. Determine if the biconditional, “A number is divisible by 6 if and only if it is divisible by 3” is true. If
false, give a counterexample.
21. Solve for x and justify each step: 4x – 5 = 2
Statement
Reason
22. Solve for x and justify each step: 3  x  2  x  2
Statement
23. Solve for x and justify each step: x  2 
Statement
Reason
2x  8
5
Reason
24. If GH has coordinates G (2, 6) and H (-1, -1) find the distance of GH. Justify each step
Statement
Reason
25. If M is the midpoint of AB and A has coordinates (-1, 0) and M has coordinates (5,4). Find point B.
Justify each step.
Statement
Reason
26. QS bisects PQR, mPQR = (6x - 4), and mSQR = (2x + 4). What is the value of x? Justify each
step.
Statement
Reason
27. D is between C and E. CE = 6x, CD = 2x + 3, and DE = 13. Find CE. Justify each step.
Statement
Reason
Chapter 3:
Vocabulary
Parallel Lines
Transversal
Same-side Interior angles
Perpendicular Lines
Corresponding Angles
Perpendicular Bisector
Skew Lines
Alternate Interior Angles
Slope
Parallel Planes
Alternate Exterior Angles
Problems
Use figure 1 to name to following:
1. Name all segments skew to WX
2. Name all segments parallel to QR
3. Name all segments perpendicular to PS
4. Name a plane parallel to plane WPS
5. Name a corresponding angle to  4
6. Name a same-side interior angle to  6
7. Name an alternate exterior angle to  2
8. Name an alternate interior angle to  4
Transversal
Classify the Pair of Angles
9.  4 and  6
10.  6 and  7
11.  2 and  3
EF
DG . Find the measure of each angle.
12. m ABE
13. m EBC
Use figure 5 to find the value of x and y. a
14.
b c
a
6x + 5y
54
b
62
x ____________
c
6x + 3y
y ____________
figure 5
15. Solve for x and y in figure 6.
E
8x + 4y
7x + 6y
D
F
x ____________
84
G
figure 6
y ____________
a) Which theorem could be used to show a b when:
b) Find the angle measure.
16.  1   3
17.  7 +  6 = 180°
m 1 = (21x + 1) and m 3 = (30x – 44)
m 7 = (12x – 8) and m 6 = (5x + 18)
a)
b)
a)
b)
8
1 2
7
3
6
4
5
figure 7
18. Complete the proof of the alternate exterior angles theorem using figure.
Given: r s
Prove:  1   2
s
2.
Reason
1.
13
3
2
Statement
1.
1
r
2.
3.
3. Vertical Angle Thm.
4.
4.
figure 8
23
1+2=3
Reflexive Prop of 
Transitive Prop of 
Corresponding
Thm
Addition Prop of 
19. Name the shortest segment, write an inequality for x, then
solve the inequality.
20. Lines p and q together contain a linear pair in
which the angles are congruent. What is the
relationship between lines p and q?
__________, _______________, ___________
Determine if line r is parallel to line t based on the given information.
If yes, state the theorem or postulate that justifies your conclusion.
21.  1  3
Yes / No ____________________________
t
r
22.  4  6
Yes / No
____________________________
1 2
3
4
23. m 3 + m 8 = 180
Yes / No
5 6
8 7
____________________________
Find the value of x that makes line r parallel to line t. Use the figure above.
24. m 3 = 8x – 7
&
m 7 = 3x + 8
25. m 2 = 7x + 10
&
m 5 = 11x – 64
Using the points, graph each pair of lines. Then use the slope formula to determine whether the lines are
parallel, perpendicular, or neither.
26.
27. JK & JL, J  4,  2 , K  4, 2 , L  4,6 
AB & CD
A  2, 1 , B  3, 4 
C  2, 3  , D  3, 6 
______________
___________
Write the equation for each line.
28. Write the equation of the line with slope
2
3
29. Write the equation of the horizontal line
passing through (2, 3) in point-slope form.
passing through (6, –4) in point-slope form.
30. Write the equation of the line passing through 31. Write the equation of the line with
(5, 2) and (–2, 2) in slope-intercept form.
y-intercept –3 and x-intercept 4 in slope-intercept
form.
Graph each line.
32. y = 2
33. y  4 
2
( x  6)
3
34. y  3 x  4
35. y  4 x
Determine whether the lines are parallel, intersecting, or coinciding.
36. y  x  7
5
37. y  x  4
y  x  3
38. x + 2y = 6
1
y   x 3
2
2
2y  5 x  4
39. 7x + 2y = 10
3y  4 x  5
Chapter 4:
Vocabulary
Acute Triangle
Equilateral Triangle
Corresponding Angles
Included Side
AAS
Vertex Angle
Equiangular Triangle
Isosceles Triangle
Corresponding Sides
SSS
HL
Base
Right Triangle
Scalene Triangle
Congruent Polygons
SAS
CPCTC
Base Angles
Obtuse Triangle
Remote Interior Angle
Included Angle
ASA
Legs of an Isosceles Triangle
Problems
Problems
Classify the following triangles by angles and sides
1.
2.
123
3.
23
67
Sketch RAD  BIG . Label all sides and angles to represent their congruence,
then complete the following congruency statements.
4.
5.
Sketch the two triangles here:

G

________________
AD  __________________
6.
IGB  ________________
7.
GB  ________________
Solve for the missing angle measures or missing variables.
8.
9.
10.
A
10x + 20
D
5x + 80
C
mD  ________________
mP  ________________
t=________________
AC  _____________________
11.
(3x + 5)
12.
2x
13.
(2x + 10)° (3x – 5)°
x  ________________
mO  __________________
x  ________________
mO  __________________
mPRS = __________________
14.
15.
16.
(2x + 3)°
77°
168°
x = __________________________
x = ______________________
mS= ___________________
w = ______________________
TS = _______________________
17 – 25: State whether each pair of triangles is congruent by SSS, SAS, ASA, AAS, or HL. If possible, write a
congruence statement for each pair of triangles. If the triangles are not congruent write “Not ” in the
blank and list any additional information you would need to be able to say the triangles are congruent.
17.
18.
19.
Q
Y
Z P
X
20.
21.
R
22.
P
L
O
N
Q
23.
24.
25.
F
E
G
H
Determine if you can prove the two triangles congruent using the given information. If they are congruent state the
theorem or postulate that justifies your answer. If there is not enough information, write none.
27. VS bisects RST and RVT
26. G  W, MA  HO ,
M
H
M  H
_____________________
________________
W
O
A
G
28. An acute angle in a right triangle has a measure of
3
10 . Find the measure of the other acute angle.
4
29. In a right triangle, the measure of one acute
angle is 31°. Find the the measure of the other
acute angle.
30. Given: FGHI is a rectangle
FI  GH , FIH and GHI are right angles
Prove: FH  GI
STATEMENTS
REASONS
1. FGHI is a rectangle
1.
2. FI  GH , FIH and GHI are right angles
2.
3.
3. Rt  Thm
4.
4. Reflexive Prop of 
5. FIH  GHI
5.
6.
6.
31. The angles of a triangle are in the ratio 5:12:13. Find
the measure of each angle.
32. Write the equation of the line with slope of –6 and y
intercept –8 in slope intercept form.
34. Write the equation of the line passing through (5, 1)
35. Write the equation of the perpendicular bisector to
the line passing through (6,0) and (0,4) in slope
intercept form.
and (8, –2) in point slope form.
Simplify the following radical expressions.
350
1.
162
2.
156
3.
4.
7 40
5.
12x 3 y 8 z 2
6. 6 25x y z
 4

4
3
2
 25
44 2

13. 9 3c
 44

11.
10
3 15c
14.
c5 d 2 e f 4
24
6
6
2
12. 3 12
c 0 e 6f 4
0
2 30
15. 4 c d e f
7
4
1
 2 c 0 e 5f 0
16.
4
18.


441

17.
2

5 
 8

125 

 6 
19. 

 11 
517 
2

1
81
20.
22. 29




24.
21.
2
x 5t 2
81t 3
23.
 54t 7

 65 x 2





25.
9
196
 87 
2
9 a4b6
81t 3
 108t 7

 64a 2




