-
mewor
have spec
meanings
math.
PRACTICE Connect eabh word on the left to its
math definition on the right.
1. Point
An endless flat surface with no thickness
2, Line· •
The part of a line from one point to another
3, Segment
A straight path that goes forever in both directions
4. Ray
Two rays that start at the same point
5. The part of a line beginning at one point
and extending forever in one direction
6. An exact location
t!ACTICE f Conn:;ch word it best describes.
7. Point 8. Line 9. Segment 10. 11. Angle
/
C D Q
•
y
L z
G H
Beast Academy Practice 4A Guide Pages: 14-18 [I
YOU co•• . - oints,
h..,... to. nome
~ P t"'""'
_.,gmen
Ii~ , hn41 on page~
ond ro'f 1 f .a. ,jde
14- 18 O 1.7""
J,A .
swer the questions that follow.
PRACTICE J use the diagram beloW to an
12. points, f<. ,J:_, and Jj
. Name the three given points
12
in the diagram above.
A line segment is named by its endpoints.
13.
The order of the points does not matter.
\(
So, segment KL can also be named segment l:.£..
14. line l,n, L&,~ ,
14.
Lines can be named using any two points on the
line. The order of the points does not matter. \<L,and !'1 L ,
, -
One way to name the line above is MK. . '
Find five other ways to name line MK. '
A ray is named by its origin and any other point on the ray.
The name of a ray always begins with the origin.
So, ray KM can also be named ray
t) Can ray LM be named any other way using the given
points? If so, give one other name. If not, explain.
fO' b-e Gt.U.1-) RJ:•.' r- ~} ( ClfAt\
-fJ (J C l( w 'c1.r J 5 1 --> v ,i
\ { \
!] Guide Pages: 14-18 Beast Academy Practice
I Name the angle in the diagram below.
--- EXAMPLE
We usually
name angles
with three poin!s:
point on one side,
vL I
z
It
"the vertex, then a An angle is named using a point on
oint on the other each side and the vertex. The vertex is
P side.
always listed in the middle . The order
of the other two points does not matter.
So, we can name the angle
above angle XYZ, or
angle ZYX.
8,
PRACTICE Use the diagram above for the problems that follow. Connect each angle
name on the left to the name on the right that describes the same angle.
I
11. angle ABO ---:- ngle ABC
v
18. angle BOC angle COB
19. angle OBC ~- ;::----,,,;IL_ y angle BOA _
' ~ ~,
20. angle CBA
/
. - rngle CBO
21. angleADB / ' \ ingle OBA
•
Angle BCD can be named four 22. angle Pc1& , A-L-8 ,
different ways. Find the three
other ways to name angle BCD. and f; L!(
Beast Academy Practice 4A Guide Pages: 14-18 [IJ
r-....
0
')
.c
"'l
...
c1
(/\
PRACTICE / Use the diagram below to answer the questions that follow.
{
(b
Vi X y z
23. Name the three different line segments 23. segments~
in the diagram above.
-lf:iz. ,and
24. There are four different rays that can be named 24. rays4-,4,
yr,
using the given points. Name them all.
and~
PRACTICE / Use the diagram below to answer the questions that follow.
,. Name three angles that have
vertex E.
25. angles H F, 6, E'H, and . S {.,J
Name all eight different angles that
can be named using the points in the
26. angles 1-r£ 6J f ·'t, f ¤ f 6)
diagram above. ~t:::t rt, .a,E~ t6t Hb and E-<
~ 1-/
Beast Academy Practice 4A
&
You can
review how to
ea5 ure an angle
~h O protractor on
wr ages 1q-24 of
p euide 4A.
z
C
PRACTICE Use the diagram above to answer the questions that follow.
Find the measure of each angle using a protractor.
Find larger versions of the diagram above along with printable protractors at BeastAcademy.com.
21. angle TCV = _iJ___ 0
28. angle ZCW = L5 P) A small
raised circle
after an angle
measurement
29. angle ZCY = 3-Q_ 0
30. angle wcx = ll 0 means
\\degrees."
r exampl
31. angle VCW = _J_°- .. \
32. angle YCT = @ 0
5°" mea
degre
PRACTICE Use your measurements above to find the measure of
each angle listed below without using a protractor.
' ~ rl
33. angle TCW =
""~(.
.J.tl
0
34. angle VCX= 'fO 0
* *36.
35. angle zcy = 1·-~7 ° angle XCY = 30°
* *
Beast Academy Practice 4A Guide Pages: 19-24 [II
PRACTICE
IUse the diagram below to answer the que stions th at follow.
You may use a protractor to measure th e angles.
A
0
Find larger versions of this diag
along with printable protractors :arn
BeastAcademy.com. t
' .
37. Which two different angles have meas~re 15°? 37. angles B2- A and f16.
38. Which two different angles have measure 60°? 38. angles f Z 6\ and --.:......:
G-ZA
39. Which two different angles have measure 165°? 39. angles £ ZB and f=ZA
40. _ Which two different angles have measure 75°? 40. angles F2M and J) 2
t1. Which two different angles have measure 45°? 41. angles f z Cr and C,,28
(2. Which two different angles have measure 135°? 42. angles F2 L a n d ~
'gJ Guide Pages: 19-24
Beast Academy Practice 4A
PRACTICE F?r ea~h problem below, use your protractor and the
given lines and points to create the diagram described.
43. Draw ray BC so that the measure of
angle ABC equals 18°.
A B
ti
44, Draw ray FH so that the measure of
angle GFH equals 80°.
45. Draw ray ML so that the measure of
angle LMN equals 170°.
•
N
•
46. Draw ray RS so that the measure of
angle ORS equals 35°. Q
Beast Academy Practice 4A Guide Pages: 19-24 [ill
'
------
''an~ e . F o
L A C rT'lea ns
L rT'l e ans
T h e sv; n b o~ ;')(arT'IPle,
" angle
ABC-"
b ut angles
Use what you know _a o below.
PRACTICE to answer the questions
47.
nd KXL in the
47. Wendy measures angles HXJ , JXK, a ures of the three
diagram below. She then adds the meas parately , find
angles . Without measuring each angle se,
the sum of the measures of the three ang es.
48. LQRS= ~
t1 ijj
48. The measure of LSRT is 50 degrees. Without using a
protractor, find the measure of LQRS.
Q R
49. Lines WY and VZ cross at point X. The measure of LVXW 49. LVXY= t l{t;~
is 35 degrees. Without using a protractor, find the measure
of LVXY, LYXZ, and LWXZ. LYXZ=
LWXZ= 1l1 \0
w y
50. What is the sum of the measures of LVXW, LVXY LYXZ 50.
-:')7 fu
and LWXZ? ' '
lliJ Guide Pages: 19-24 Beast Academy Prac
we can label
tt,e meofure of an
angle with o small
cur,,<e called an For example,
ttre. the measure of
angle A8C can
be labeled as
shown.
PRACTICE Use what you know about angles to answer the questions below.
Ella measures angles ANG, GNL, LNE, and ANE in the
diagram below. She then adds the measures of the four
angles. Without measuring each angle separately, find
the sum of,the measures of the four angles.
52, Segment GE connects opposite corners of square DEFG. 52. LEGF= 4S)' G I
* Without using a protractor, find the measure of LEGF,.
/ f
53.
*
Segment EG connects opposite corners of rectangle EFGH.
The measure of angle FEG is twice the.measure of angle GEH.
53. LFEG= 60
Without using a protractor, find the measure of LFEG .
V
F,........_ _ _ _ _ __
q,~
q +6
~;... '.Lb St, E H
Beast Academy Practice 4A
OI
=
PRACTICE Use what you know about angles and triangles to
answer the questions below withouts protractor.
57. In triangle ABC, the measure of angle ABC is
· 57 degrees, and the measure of angle BCA is 43 degrees.
57. LBAC= g0
What is the measure of angle BAC?
58. '
In right triangle XYZ, angle x'v-z is the right angle. What is the
sum of the measures of the other two angles in triangle XYZ?
X
59- Every equilateral triangle has three equal sides. The three ss. __,_6"---D
__
angles of an equilateral triangle are also equal. What is the
measure of each angle in an equilateral triangle?
/i2; b .,._;, 01,)\
1 t)
60. In triangle PQR, angle QPR is 60° greater than angle PRQ. 60. LP RQ = ___,,,
') __;::·,.= ---
* Angle PBR is 30° less than angle PRQ.
What is the measure of angle PRQ? b t'(
p C\ = b 60
l Q~-R-h
.
0 (-
Beast Academy Practice 4A 20
··"
'
I
I
..
I,
''
s-- @]
_, -~ '
'-·
\
I
the questions that follow
answer .
I be10W to
n1atera
quad
PRACTICE I use the L
JL-----
61. LJKL:: tt{0 °
asure of each angle in
61. Use a protractor to find the me
LKLM::~
the quadrilateral above.
LJML::~
LKJM= coi
62.
62. What is the sum of the measures of the four
angles in quadrilateral JKLM?
63. Every rectangle has four right angles. Is the sum of the angle
xf5o'
63. __,,,_
, __
measures in a rec.tangle more, less, or the same as the sum of the
angle measures in quadrilateral JKLM above?
The su~
Beast Academy Practice 4A
PRACTICE I Use the quadrilate;a, below to answer the questions that follow.
Answer the questions withouts protractor.
z
.
64. Draw segment WY to split quadrilateral WXYZ into two
triangles. The measure of angle XYW is 50°. Find the
. 64. LXWY= fO
measure of angle XWY . .
@ Find the measure of angle zvw. ~o
65. LZYW= - - -
~ . The measure of angle WZY is 60°. Use your answer to the 66. LZWY = ~ l ti
·V previous question to find the measure of angle ZWY.
J
67. What is the sum of the measures of the four
angles in quadrilateral WXYZ?
68. Any quadrilateral can be split into two triangles by connecting two
/ opposite corners with a line segment. For example,
£ya
A
-D C
Using what you learned on the previous pages about the sum of the
angle measures in a triangle, what can you conclude about the sum I I
of the angle measures in a quadrilateral? 11,-e. q/ y l.\4j' 5
d, d I). Up
fo 360~ ctVl <A c CAh p.e, f fJ ,11eJ :v-i +-~
st Academy Practice 4A
rt, ot;vtt,IB ) Q;( l~ 1-iave '~ Si J es, r:;-;;i19 1
