Download Geometry Fall 2015 Lesson 046

Midterm Review (Answer Key)
Per _____Name ___________________
o
1) In the diagram of SDU , m  SDU  90 and
m  SUD  62 o . TY is drawn connecting points T and
o
Y on the triangle, such that m  SYT  53 . Find
m  UTY
m<UTY = 81o
2) Point P divides any triangle ABC into 6 triangles of equal area.
To locate point P, what should one construct?
A) Perpendicular bisectors
B) Centroid
C) Altitudes
D) Incenter
E) Parallel Lines
B) Centroid
*3) Write a conditional statement that is logically equivalent to “If the negotiations fail, the baseball
strike will not end.”
If the baseball strike ends, then the negotiations will not fail.
4)Lines s, m and n are concurrent and lines s and m intersect line r
at points X and Y. Find m  Z.
m<Z = 74o
5) State the degree(s) of rotational symmetry for a regular pentagon
72o
,
144o
,
216o
,
288o
*6) Write a conditional statement, that is based on a theorem or
definition, using the numbered angles below that would prove lines
j and k parallel.
Possible Answer: If 2 lines, such as j and k, are cut by a transversal
forming congruent alternate interior angles, such as 2 and 7, then the
lines are parallel.
7) The diagram at the right shows
MOS with MOU
.
OE  MS . If m  SOE  58 and  MOE  SOE , find m  M
o
m<M = 32o
8) Which two points determine the
perpendicular bisector of
3
,
AB ?
8
Questions 9-11 refer to the diagram and two column proof below.
Statements
Reasons
1. K is the midpoint of
1. Given
HK  JK
3.  H  J
2.
2.
HJ
( s.  s.)
( a.  a.)
4.
 JI
5. IF  IG
4. HI
6.
3. Given
5. Given
HI  IF  JI  IG
6.
or
HF  JG
( s.  s.)
7. HFK  JGK
8.
FK  GK
7. SAS Postulate
(2,3,6)
8. Corresponding parts of congruent
triangles are congruent.
(7)
9) What reason best justifies statement (2) in the proof?
Definition of a midpoint – A midpoint divides a line segment into 2 congruent segments.
10) What reason best justifies statement (4) in the proof?
Converse of the Isosceles Triangle Theorem – If two angles of a triangle are congruent, then the
angles opposite those sides are congruent.
11) What reason best justifies statement (6) in the proof?
Subtraction Postulate – If equal quantities are subtracted from equal quantities, the differences are
equal.
*12) Given regular hexagon ABCDEF with center G, write a transformation that maps triangle 4
onto triangle 6.
TCG 4  6
or
RG, 120o 4  6 are possible answers.
*13) In the diagram at the right, list 3 points which are
coplanar.
Any 3 points, such as C, B, and D
14) In the diagram at the right, LMA is isosceles with
LM  AM , m  L  37 o and m  AMO  19o .
What is
m  LMO ?
m<LMO = 87o
15) Find the degree measure of <REA in the figure at the
right.
(This question refers to acute  REA outside
pentagon GREAT)
m<REA = 70o
16) Write sequence of rigid motions in function notation that
k.' o' p '
kop
could potentially map sector
onto sector
r
perp.bis.o 'k '
T kop
ok '
PHI , m  P  x , m  H  3x and m  I  50 . Which statement is true?
PHI is an equilateral triangle
17) In
2
(1)
(2) PH < HI < PI
(3)  P  H
(4) PHI is an obtuse triangle
(4) PHI is an obtuse triangle
18) For what values of x and y will
MG and NJ be parallel?
x  16 , y  20
19)
(1) one
*20) Write a transformation that maps quadrilateral
AERO onto quadrilateral OBIC.
TAO  AERO   OBIC
21) Given right TSE , GO  5x and GO  15x 12 . Find the
length of GS
GS = 18
22) Given the statement: “If the acute angles of a triangle are complementary,
then the triangle is a right triangle.” What is the truth value about the statement
and the truth value of its converse?
True
True
23) Given:
GE
AD  FC
Which is a valid conclusion?
(1)  GBC  EBF
(2) <ABF is complementary to <DBC
(3) m<GBC +m<ABE =180o
(4) m<FBE=m<GBA
(1)  GBC  EBF
24)
2) Parallel
25) What is the difference between the sum of the measures of the interior angles of a
regular octagon and the sum of the measures of the exterior angles of a regular octagaon?
720o
26) The angle bisector of angle B goes through
which point?
H
27) For what values of x and y
will the lines L1 and L2 be perpendicular?
x  10 , y  20
*28) and 29)
Given:
 1 is supplementary to  2
 3  1
Prove:
AD || BC
Statements
1) Given
2) <3  <1
2) Given
3) m<1 + m<2 = 180
3) Definition of supplementary angles. (1)
4) m<3 = m<1
4) Definition of congruent angles.
5) m<3 + m<2 = 180
5) Substitution Postulate
6) <3 is supplementary to <2
6) Definition of supplementary angles. (5)
7)
AD || BC
30) In the figure at the right, PA  3x 2 , PB  7 x  6
y
and PC  . Find the value of y.
2
y = 54
Reasons
1) <1 is supplementary <2
(2)
(3, 4)
7) If two lines are cut by a transversal
forming interior angles on the same side
of the transversal that are supplementary
then the lines are parallel.
(6)
31) Given the figure at the right, find m  FTO .
m<FTO = 80o
32)
.
Find m  z
m<z = 131o
33)
(2)
Answer Sheet
No.
1
Answer
No.
18
Answer
x = 16, y = 20
2
3
(B) Centroid
19
20
(1) One
* T  AERO   OBIC
4
m  Z  74
21
GS  18
5
6
72 , 144 , 216 , 288
*
7
m  M  32o
22
23
24
True, True
(1) <GBC  <EBF
(2) Parallel
8
9
10
11
12
3, 8
Definition of a midpoint
25
26
27
28
29
720o
H
x = 10, y = 20
*Proof
*Proof
13
*Any 3 points such as CBD
m  LMO  87
m  REA  70o
30
31
y = 54
14
32
m  z  131o
33
(2) Rotation
15
16
17
m  UTY  81o
* If the baseball strike ends, then the negotiations will not fail.
o
o
o
o
o
Converse of the Isosceles Triangle Theorem
Subtraction Postulate
*T
CG
*
r
4  6
perp.bis.o 'k '
o
T kop
ok '
(4) PHI is an obtuse triangle
AO
m  FTO  80o