writing: answer each question with complete sentences...
TRANSCRIPT
Honors Geometry 1st Semester Review Packet
Writing: Answer each question with complete sentences.
1) Explain what it means to bisect a segment. Why is it impossible to
bisect a line?
2) Are all linear pairs supplementary angles? Are all supplementary angles
linear pairs? Explain.
3) Explain why a four-legged table may rock from side to side even if the
floor is level. Would a three-legged table on the same level floor rock
from side to side? Why or why not?
4) Can two planes intersect in a segment? Explain.
Short Answer: Answer each question completely.
5) Sketch the figure described.
Three lines that lie in a plane and intersect at one point
6)
Use the figure to the right to answer the
following questions.
a) Name the intersection of plane CDF and
plane BAD.
b) Are the points B and F collinear?
c) Are the points B and F coplanar?
d) Name three planes that intersect at
point A.
Honors Geometry 1st Semester Review Packet
7) Point S is between R and T on RT . Use the given information to write
an equation in terms of x. Solve the equation. Then find RS and ST.
RS = 2x + 10
ST = x – 4
RT = 21
8) Point M is the midpoint of RT . Find RM, MT, and RT.
9) The endpoints of two segments are given. Find the length of the
segment rounded to the nearest tenth. Then find the coordinate of
the midpoint of the segment.
A(2, 5) and B(4, 3)
10) Point C(3, 8) is the midpoint of AB . One endpoint is A(-1, 5). Find the
coordinates of endpoint B.
11) Find ABCm and CBDm if ABDm = 120.
12) VZ bisects UVW , and oUVZm 81 . Find .UVWm Then classify
UVW by its angle measure.
Honors Geometry 1st Semester Review Packet
13) If 2m = 6x - 1 and the 4m = 4x + 17, then find the 3m .
14) 21 and are complementary angles. Find the measures of the angles
when oxm )10(1 and o
xm )402(2 .
15) Pentagon ABCDE is a regular polygon. The length of BC is represented
by the expression 5x – 4. The length of DE is represented by the
expression 2x + 11. Find the length of AB .
16) Draw a sketch of a concave pentagon.
17) Draw an example of a linear pair.
Fill-in the blank: Fill in the blank with the most appropriate word.
18) A ___________ has a definite beginning and end.
19) A ____________ has a definite starting point and extends without
end in one direction.
20) ___________ are two rays that are part of the same line and
have only their endpoints in common.
21) You can use a _________ to measure angles and sketch angles of
given measure.
22) Angles with the same measure are ____________________.
23) Two angles are __________________ if and only if (iff) the
sum of their degree measure is 180.
24) A regular polygon is both ___________ and ___________.
25) Describe the pattern in the numbers. Write the next three
numbers.
-6, -1, 4, 9, …
Honors Geometry 1st Semester Review Packet
26) Write the if-then form, the converse, the inverse, and the
contrapositive for the given statement.
All right angles are congruent.
If-then:
Converse:
Inverse:
Contrapositive:
27) If you decide to go to the football game, then you will miss band
practice. Tonight, you are going to the football game. Using the Law of
Detachment, what statement can you make?
28) If you get an A or better on your math test, then you can go to
the movies. If you go to the movies, then you can watch your favorite
actor. Using the Law of Syllogism, what statement can you make?
29) Show that the conjecture is false by finding a counterexample.
The sum of two numbers is always greater than the larger number.
Use the diagram to write examples of the stated
postulate.
30) A line contains at least two points
31) A plane contains at least three noncollinear
points.
32) If two planes intersect, then their
intersection is a line.
Honors Geometry 1st Semester Review Packet
2
33) Sketch a diagram that represents the given information:
straight angle CDE is bisected by DK .
Solve the equation. Write a reason for each step.
34) -7(-x + 2) = 42
Name the property illustrated by the statement.
35) If DEFJKLJKLDEF then ,
36) CC
37) If om 574 , find .3and,2,1 mmm
38) Find the measure of each angle in the diagram.
Short answer: Answer the following questions using complete
sentences.
39) How can you show that the statement, “If you play a sport, then
you wear a helmet.” Is false? Explain.
40) Use deductive reasoning to make a statement about the picture.
1 4
3
7y - 12
4x 6y + 8
6x - 26
Honors Geometry 1st Semester Review Packet
41) What is a theorem? How is it different from a postulate?
42) Explain why writing a proof is an example of deductive
reasoning, not inductive reasoning.
43) Describe the relationship between the angle measures of
complementary angles, supplementary angles, vertical angles, and
linear pairs.
44) Complete the following proofs.
a) Given : AC = AB + AB
Prove: AB = BC
Statements Reasons
1. AC = AB + AB 1. Given
2. AB + BC = AC 2.
3. AB + AB = AB + BC 3. Transitive Property of Equality
4. AB = BC 4.
b) Given: AB is a line segment
Prove: AB AB
Statements Reasons
1. AB is a line segment 1. Given
2. AB is the length of AB 2. Ruler Postulate
3. AB = AB 3.
4. AB AB 4.
B
Honors Geometry 1st Semester Review Packet
c) Given: ,A B B C
Prove: A C Statements Reasons
1. ,A B B C 1. Given
2. ,m A m B m B m C 2.
3. m A m C 3. Transitive Property of Eq.
4. A C 4.
45) Complete the statement.
a. 3 and _____are corresponding angles.
b. 4 and _____are consecutive interior angles.
c. 6 and _____ are alternate interior angles.
d. 1 and _____are alternate exterior angles.
46) Find the value of x. Explain your reasoning.
47) Find the value of x. Explain your reasoning.
48) Find the value of x. Explain your reasoning.
Honors Geometry 1st Semester Review Packet
Find the value of x that makes m n .
49)
50)
51)
52) A line that intersects two other lines is a _______________.
53) Find the values of x and y.
54) Find the values of x and y.
55) Draw a pair of parallel lines with a transversal. Identify all pairs
of alternate exterior angles.
Honors Geometry 1st Semester Review Packet
56) What angle pairs are formed by transversals?
57) Michaela was stenciling this design on her bedroom walls. How
can she tell if the top and bottom lines of the design are parallel?
58) In the figure each rung of the ladder is parallel to the rung
directly above it. Explain why the top rung is parallel to the bottom
rung.
59) How do you find the slope of a line given the coordinates of two
points on the line?
60) Find the slope of the line that passes through the points
(3, 5) and (5, 6).
Tell whether lines through the given points are parallel, perpendicular,
or neither. Justify your answer.
61) Line 1: (1, 0), (7, 4)
Line 2: (7, 0), (3, 6)
62) Line 1: (-3, 1), (-7, -2)
Line 2: (2, -1), (8, 4)
63) Graph the line through the given point with the given slope.
P(3, -2), slope: -3
Honors Geometry 1st Semester Review Packet
64) Write an equation of the line in slope-intercept form passing
through the point (2, -3) that is parallel to the line with the equation
y = 6x + 4.
65) Write an equation of the line in slope-intercept form passing
through the point (3, -4) that is perpendicular to the line with the
equation 1
12
y x .
66) What does intercept means in the expression slope-intercept
form? Use complete sentences.
67) Graph the equation 2x + 3y = 12 by finding the x- and y-
intercepts.
68) The ______________________ segment is the shortest
distance between a point and a line.
69) In the diagram, AB BC . Find the value of x.
70) Find the measure of the indicated
angle.
a) Angle 2
b) Angle 5
c) Angle 3
Honors Geometry 1st Semester Review Packet
71) Complete the proof.
Given: 1 115 , 2 65o o
m m
Prove: m n
72) Can a right triangle also be obtuse? Explain why or why not.
73) What must be true of a transformation for it to be a rigid
motion?
74) List three examples for transformations that are rigid motions.
75) How can you use side lengths to prove triangles congruent?
76) A triangle with three congruent sides is called ____________.
77) Describe the difference between isosceles and scalene
triangles.
78) Compare vertex angles and base angles.
79) Sketch an acute scalene triangle. Label its interior angles 1, 2,
and 3. Then draw and shade its exterior angles.
Find the value of x. Then classify the triangle by its angles.
80)
n
m 1
2
Honors Geometry 1st Semester Review Packet
81)
82)
83)
In the diagram, QRS XYZ
84) Find m R
85) Find XY
86) Find m X
87) Find m S
88) Write all the congruence statements for the figures.
89) Identify the transformation you could use to move the solid figure onto
the dashed figure.
Honors Geometry 1st Semester Review Packet
90) Find the values of x and y. A B C D E F G H
91) The picture below shows a gate from Fort Meigs Museum in Perrysburg,
Ohio. Using what you have learned in this chapter, explain why the builder
would put in the diagonal crosspiece on the gate.
92) GIVEN: ,M N PQ M Q N P
PROVE: MNQ PQN
93) Explain the difference between proving triangles congruent using the
ASA and AAS Congruence Postulates.
94) You know that a pair of triangles has two pairs of congruent
corresponding angles. What other information do you need to show
that the triangles are congruent?
95) How can you use congruent triangles to prove angles or sides
congruent?
Honors Geometry 1st Semester Review Packet
96) The angle between two sides of a triangle is called the ___________
angle.
97) Corresponding parts of congruent triangles are ________________.
Use the given information to name two triangles that are congruent, if
possible. Explain your reasoning.
98) RSTUV is a regular pentagon.
99)
100)
101)
102)
V
U
T
S
R
Q
D A
U
D C
B
A
S
T
R
A
P
H
T A
M
Honors Geometry 1st Semester Review Packet
103) Prove that TURRST .
104) Prove that DBCABC .
105) Given: 21 andARAC
Prove: 43
106)
Given: UGBU ; BGtsbiUM sec
Prove: MUGBUM
107) Given: B is the midpoint of CD ; 21
Prove: EA
R
T
U
S
D C
B
A
S
R
A
L
C 2
4
3
1
M
U
G B
2
E
D
C
A
B
1