Download Geometry Fall 2016 Lesson 048

Midterm Review
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
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
3)
4)Lines s, m and n are concurrent and lines s and m intersect line r
at points X and Y. Find m  Z.
5) State the degree(s) of rotational symmetry for a regular pentagon
,
6)
,
,
7) The diagram at the right shows
MOS with MOU
.
OE  MS . If m  SOE  58 and  MOE  SOE , find m  M
o
8) Which two points determine the
perpendicular bisector of AB ?
,
Questions 9-11 refer to the diagram and two column proof below.
Statements
1. K is the midpoint of
Reasons
HJ
HK  JK ( s.  s.)
3.  H  J ( a.  a.)
2.
4. HI
1. Given
2.
3. Given
4.
 JI
 IG
6. HI  IF  JI  IG
5. IF
5. Given
6.
or
HF  JG ( s.  s.)
7. HFK  JGK
8.
FK  GK
9) What reason best justifies statement (2) in the proof?
10) What reason best justifies statement (4) in the proof?
7. SAS Postulate
(2,3,6)
8. Corresponding parts of congruent
triangles are congruent.
(7)
11) What reason best justifies statement (6) in the proof?
12) Given regular hexagon ABCDEF with center G, write a transformation that maps
on to AGB .
EGF
13) In the diagram at the right, which points which are
coplanar.
A) FDEAG
B) CDAGH
C) IHCDE
D) CDF
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 ?
15)Find the degree measure of <REA in the figure at the
right.
(This question refers to acute  REA outside
pentagon GREAT)
16)Write sequence of rigid motions in function notation that maps ABC onto DEF .
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
18) For what values of x and y will
MG and NJ be parallel?
19)
20)Write a transformation that maps quadrilateral AERO
onto quadrilateral OBIC.
21)Given right TSE , GO  5x and GO  15x 12 . Find the
length of GS .
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?
23)
24) 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
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?
26) The angle bisector of angle B goes through
which point?
27)For what values of x and y
will the lines L1 and L2 be perpendicular?
Statements
1)  1 is supp. to  2
Reasons
1)
2)  3  1
2)
3) m  1  m  2  180
3)
4) m  3  m  1
4)
5) m  3  m  2  180
5)
6)  3 is supp. to  2
6)
28) and 29)
Given:
7) AD || BC
7)
 1 is supplementary to  2
 3  1
Prove:
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
31) Given the figure at the right, find m  FTO .
32)
33)
. Find m  z
Answer Sheet
No.
1
2
3
Answer
4
5
6
7
8
9
mZ 
10
11
12
13
14
15
16
17
m  UTY 
mM 
Name _____________________ Per_____________
No.
18
19
20
Answer
X=
21
22
23
24
25
26
GS 
27
28
29
m  LMO 
m  REA 
30
31
32
33
y=
*See Proof Statements 1-4
*See Statements 5-7
y=
m  FTO 
m z 