Geometry 1 Semester Review Packet: Completed review...
Transcript of Geometry 1 Semester Review Packet: Completed review...
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
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.
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
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
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 o
UVZm 81 . Find .UVWm Then classify UVW by its angle measure.
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 .
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
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, …
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:
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
2
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.
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 o
m 574 , find .3and,2,1 mmm
38) Find the measure of each angle in the diagram.
1 4
3
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
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.
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 one of 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.
7y - 12
4
x 6y + 8
6x - 26
B
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
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.
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.
1) Complete the statement.
a. 4 and _____are corresponding angles.
b. 3 and _____are consecutive interior angles.
c. 5 and _____ are alternate interior angles.
d. 7 and _____are alternate exterior angles.
2) Find the value of x. Explain your reasoning.
3) Find the value of x. Explain your reasoning.
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
4) Find the value of x. Explain your reasoning.
the value of x that makes m n . Find
5)
6)
7)
8) A line that intersects two other lines is a _____________________.
9) Find the values of x and y.
10) Draw a pair of parallel lines with a transversal. Identify all pairs of
alternate exterior angles.
11) What angle pairs are formed by transversals?
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
12) Michaela was stenciling this design on her bedroom walls. How can she
tell if the top and bottom lines of the design are parallel?
13) 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.
14) How do you find the slope of a line given the coordinates of two points
on the line?
15) 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.
16) Line 1: (1, 0), (7, 4)
Line 2: (7, 0), (3, 6)
17) Line 1: (-3, 1), (-7, -2)
Line 2: (2, -1), (8, 4)
18) Graph the line through the given point with the given slope.
P(3, -2), slope: -3
19) 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.
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
20) 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 .
21) What does intercept means in the expression slope-intercept form?
Use complete sentences.
22) Explain how you can use the standard form of a linear equation
to find the intercepts of a line. Use complete sentences.
23) Draw a line with an undefined slope on the coordinate plane.
24) The ______________________ segment is the shortest
distance between a point and a line.
25) In the diagram, AB BC . Find the value of x.
26) Can a right triangle also be obtuse? Explain why or why not.
27) What must be true of a transformation for it to be a rigid
motion?
28) List three examples for transformations that are rigid motions.
29) How can you use side lengths to prove triangles congruent?
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
30) A triangle with three congruent angles is called ___________.
31) Describe the difference between isosceles and scalene triangles.
32) Draw right isosceles triangle.
33) Draw an acute scalene triangle.
Find the value of x. Then classify the triangle by its angles.
34)
35)
36)
37)
38) Find the measure of angle 1.
1
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
39) Find m JKM.
40) Write all the congruence statements for the figures.
41) Identify the transformation you could use to move the solid figure onto
the dashed figure.
42) Find the values of x and y. ABC D EFG H
43) Explain why the bench with the diagonal support is stable, while the one
without support can collapse.
44) Explain how you could show that the triangles are congruent in the
figure.
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
45) Explain the difference between proving triangles congruent
using the ASA and AAS Congruence Postulates.
46) 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?
47) Explain what CPCTC is and why is it useful?
48) The angle between two sides of a triangle is called the
_________________ angle.
49) Are isosceles triangles always acute triangles? Explain your
reasoning.
Use the given information to name two triangles that are congruent, if
possible. Explain your reasoning by stating the postulate and the
congruence statements for the sides and/or angles that you used.
50) RSTUV is a regular pentagon.
51)
V
U
T
S
R
Q
D A
U
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
52)
53)
54)
55)
State the third congruence that must be given to prove that
DEFABC using the indicated postulate.
Given: __________,, FECBDEAB
Use the SSS Congruence Postulate.
Given: __________,, FDCADA
Use the SAS Congruence Postulate.
Given: __________,, EBEFBC
D C
B
A
S
T
R
A
P
H
T A
M
F
E
D
C
B
A
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
Use the ASA Congruence Postulate.
Find the values of x and y.
56)
57)
58) Find the values of angles 1, 2, 3, and 4.
59) Choose two proofs to complete by filling in
the blanks. You may choose to do more than the required two for
extra credit.
a) Prove that TURRST .
Statements Reasons
1. ________________ Given
2. RT TR ______________
R
T
U
S
D
U
M
5 5
5
3xo
yo
55o
(x+7)o
yo
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
3. TURRST ______________
b) Prove that ABD CBD .
Statements Reasons
1._______________ Given
2. AD B C D B All right angles
are congruent
3. _____________ reflexive prop
of congruence
4. ABD CBD _______
c) Given: UGBU ; BGtsbiUM sec
Prove: MUGBUM
Statements Reasons
1. UGBU , BGtsbiUM sec given
2. BM GM Definition of a bisector
3. __________________ reflexive property of congruence
4. BUM M UG _________________
5. MUGBUM _________________
U
D C
B
A
M G B
Geometry 1st Semester Review Packet: Completed review packets are worth 20 points
extra credit (on 3rd
quarter homework grade) and are due the day of the exam. No late
review packets will be accepted for any reason. Note: Extra credit is only available for
regular Geometry and concepts Geometry.
d) Given: B is the midpoint of CD ; 21
Prove: EA
Statements Reasons
1. B is the midpoint of CD ; 21 given
2. BC BD definition of midpoint
3. C BA D BE _____________________
4. C BA D BE _____________________
5. EA _____________________
NOTE: This review packet does not include material for chapter 5 or
chapter 6. The 1st semester exam will cover material from all topics covered
in 1st semester.
2
E
D
C
A
B
1