#### Transcript Midterm Exam Review

```Midterm Exam Review
34 questions
Slides 2 - 14
Geometry Honors
Mrs. Tiesi
Warm-up (12/7 – 12/11)
Chapter 3
1) Write an equation in slope-intercept form for a line perpendicular to
a) y = (3/4)x + 2 containing (6, 5).
b) y = (1/3)x + 2 containing (8, 9).
2) Determine whether lines AB and CD are parallel, perpendicular, or neither.
a) A(1, 5), B(4, 4), C(9, -10), D(-6, -5)
b) A(4, 2), B(-3, 1), C(6, 0), D(-10, 8)
3) Find the distance between each pair of parallel lines with the given equations.
a) y = 5x - 22 and y = 5x + 4
b) y = (1/3)x - 3 and y = (1/3)x + 2
Hint: Find the slope-intercept equation of line p (perpendicular to line a at the same y-intercept (0, b)). Solve a sytem of equations (to find an
intercepted point (x, y)) using the equations of lines b and p. Use the Distance Formula for 2 points (0, b) and (x, y) to find the answer.
4) Given the following information, determine which lines, if any, are parallel. State the postulate or
a)
<5 and <16; <6 and <13; <9 and <13; <4 and <5
b)
<7 and <2; <11 and <15; <3 and <6; <4 and 11
m
n
d
c
Chapters 1 & 4
2-column & Flow proof
5) Sec 2-6: Write a 2-column proof
a) If -4(x - 3) + 5x = 24, then x = 12.
b) If (8 – 3x) / 4 = 32, then x = -40.
6) (Sec 4-4 and 4-5) Write a flow proof
a) Given: BA = DC, <BAC = <DCA
Prove: BC = DA
b) Given: R is the midpoint of QS,
<PQR = <TSR
Prove: ∆PRS = ∆TRS
A
B
D
C
S
P
R
Q
T
B
C
7) Given: AB = DC;
=
D Prove: ∆ABD ˜ ∆CDB
A
X
Y
B
Z
8) Given:
∆ZBX ˜= ∆WBY
<ZXY = <WYX
Prove: ∆ZXY ˜= ∆WYX
W
Points, lines and planes
9) Name a point on line m.
B
10) Using AI and FE,
Name a pair of acute vertical
angles
Name a pair of obtuse vertical
angles
F
H
D
C
A
G
E
m
H
V
11) Identify a parallel plane to
plane QWM.
Identify all intersecting planes
to plane AVS.
12) Identify all skew lines to
AV.
I
S
A
W
Q
M
P
Volumes/Surface Areas of all solids
13) Baseballs and softballs come in different sizes for
different types of leagues. If the diameter of a baseball is
5 inches and a softball has a diameter of 5.4 inches, find
the difference between the volumes of the two balls.
Round to the nearest tenth (V = 4πr3/3).
14) Cakes are stacked in 2 layers as a cylinder. If the radius
of a cake is 10 inches and its height is 12 inches, find the
surface area of the frosting (T = 2πrh + 2πr2).
15) A rectangular prism pool needs to be painted. If the
bottom of the pool has dimensions 15 ft x 20 ft, and its
height is 8ft, find the paint area. (Paint Area = Ph + B ;
P = 2l + 2w ; B = l ● w)
Chapter 1
Distance, Midpoint and Slope Formulas
16)
a) A segment has a midpoint at (3, 9) and an
endpoint at (14, -8), what is the other endpoint?
b) Find the distance between 2 points: (3, 9) and
(14, -8).
c) Find the slope between 2 points: (3, 9) and (14,
-8)
Triangle Problems
17) Use Angle Sum Theorem to find <A of ∆ABC, given <B = 750 and
<C = 350.
18) Classify the triangle by its angles.
<A = 10º, <B = 160º, <C = 10º
<A = 60º, <B = 60º, <C = 60º
<A = 70º, <B = 50º, <C = 60º
<A = 60º, <B = 30º, <C = 90º
19) Classify the triangle by its sides.
AB = 1/3 cm , BC = 1/3 cm, AC = ½ cm
AB = 8 in, BC = 10 in, AC = 12 in
AB = 2.1 ft, BC = 2.1 ft, AC = 2.1ft
20) ∆ABC is an isosceles right triangle. <B is the vertex right angle. If AB = 4x –
1, BC = 2x + 5 and AC = 8x – 8.44, find x and all sides. Also, what is the
measurement of <A or <C?
21) ∆ABC is an equilateral triangle. If <A = 4x, solve for x. If AB = 3y – 10, BC
= 2y + 5, and AC = y + 20, find y and all sides.
Chapter 1
Polygons
22) Identify the polygon names,
concave/convex, regular/irregular
Chapter 4
Exterior Angle Theorem
23) Use Exterior Angle
1
Theorem,
If <3 = 80º, <6 = 108º, find <2.
If <7 = 30º, <5 = 70º, find <4.
3 5
2
4 6
7
8
The rest of the problems
24) Given <1 and <2: State the theorems/postulates (Complement, Supplement, Vertical,
Corresponding, Alternate Interior, Alternate Exterior, Consecutive Interior angles) for each
of the following statement:
<1 = <2
<1 + <2 = 90º
<1 + <2 = 180º
25) Find the Volume and Surface Area of a cylinder, given r = 10cm, h = 8cm.
26) Find the Volume and Surface Area of a rectangular prism, given length = 11cm, width = 7cm
and height = 5cm.
27) Find the base of a triangle, given h = 10cm and A = 200cm2.
28) Find the width of a rectangle, given w = 11 in and A = 132 in2.
29) Find the diagonal of a square, given A = 100cm2
30) Write a converse, inverse and contrapositive of the following statement: If you are a dancer,
then you love to dance.
31) Identify the number properties:
a)
A number is equal to itself.
b)
If 6 = x, then x = 6.
c)
If x = 3 + 5 and 3 + 5 = 8, then x = 8.
d)
If x = 3 + 5 and 8 = 3 + 5, then x = 8.
Chapter 4
32)
a) Position and label an isosceles triangle
ABC with a base BC of 2a.
b) Position and label an equilateral triangle
ABC with a side of 2a.
33) Prove 3 points form a right
triangle
P(0, 0), N(3b, 0), M(0, 2a)
• Find the slopes of all 3 sides.
• Check if 2 sides form perpendicular lines.
– 1 slope is zero and the other is undefined.
– 1 slope is the reverse reciprocal of the other.
Chapter 9
34) Given an original point of (2, -4)
a) Reflection over the x-axis, y-axis, y = x, y
= 1, x = -2.
b) Translation using a component vector <3, 2>
c) Rotation 90, 180 and 270
Notes
Chapter 4
Proving triangles congruent
a) 5 methods:
Congruent Triangles: all corresponding angles
and sides are congruent.
SSS: 3 pairs of corresponding sides
SAS: 2 pairs of corresponding sides, the included
angle is between 2 sides.
ASA: 2 pairs of corresponding angles, the included
side is between the 2 angles.
AAS: 2 angles and 1 non-included side.
b) CPCTC: Corresponding parts of congruent
triangles are congruent.
A
C
B
1 2
E
SAS
Ex: Given: AB = BD
EB = BC
Prove: ∆ABE =
˜ ∆DBC
Our Outline
P rerequisites
D S ides
A ngles
S ides
Triangles =˜
C Given: CX bisects ACB
A
˜
B
=
12
Prove: ∆ACX ˜=∆BCX
AAS
A
X
B
P CX bisects ACB
A
1= 2
A
A= B
S
CX = CX
∆’s ∆ACX =˜ ∆BCX
Given
Def of angle bisc
Given
Reflexive Prop
AAS
POLYGON NAMES
NAMES
TRIANGLE
PENTAGON
HEXAGON
HEPTAGON
OCTAGON
NONAGON
DECAGON
HENDECAGON
DODECAGON
N – GON
#SIDES
3
4
5
6
7
8
9
10
11
12
N
SEE PAGE 57 IN
TEXTBOOK
CONCAVE
CONVEX
Regular or Irregular polygons
• An Equilateral polygon: all sides are
congruent.
• An Equiangular polygon: all angles are
congruent.
• A regular polygon: a convex polygon with
all congruent sides and angles.
• An irregular polygon: is a polygon that is
not regular.
Isosceles, Equilateral Triangles
vertex angle
A
B
leg
leg
base angles
A
base
C
B
C
Area of a Triangle
A = ½ bh.
A = ½ (23 ft)(6 ft)
A = 69 ft 2
6 ft. Height
Base
23 ft.
A = ½ bh.
Area of a Square and a Rectangle
width = 10cm
side = 8cm
length = 18cm
A = s2
A=l●w
A = (8cm)(8cm)
A=
64cm2
A = (18cm)(10cm)
A = 180cm2
Find L, B, S and V
L = 2rh =
2(3.14)(6)(9)
6ft
= 339.12ft2
B = r2
= 3.14(6)2
= 113.04ft2
9ft
S = L + 2B
= 339.12ft2 + 2 ●113.04ft2
= 565.2ft2
V = Bh
= 113.04 ● 9
= 1017.4ft3
Find P, B, L, S and V of a prism
Base shape is a rectangle
P = 2l + 2w
L = P●h
5cm
B = l●w
S = L + 2B
3cm
4cm
V = B●h
Important Properties
•
•
•
•
Reflexive : a = a
Symmetric : if a = b then b = a
Transitive : if a = b and b = c then a = c
Substitution : if a = b then a may be used in