Download Triangles Student Module

Triangles Student Module
1.
Classify each triangle by its angles and sides.
a.
b.
8
8
51
7
7
8
2.
c.
9.9
35
27
Name a complementary pair of angles and a supplementary pair of
angles in the figure below.
C
D
40
50
A
B
3.
E
Refer to the figure to answer the following questions.
a.
Name a pair of vertical angles.
b.
Can you assume that YUW and WUV are supplementary from
the figure? Explain.
c.
Which angle is complementary to YWT?
d.
Identify a pair of angles that are congruent.
e.
Are YWU and UWZ:
i.
congruent?
iv.
complementary?
ii.
adjacent?
v.
supplementary?
iii.
vertical?
vi.
a linear pair?
X
V
T
Y
U
W
Z
4.
Refer to the figure to answer the following questions.
a.
Can you determine that SRP and PRT are complementary
from the figure? Explain.
b.
Name two angles that are adjacent, but not complementary or
supplementary.
c.
Given that Q and QPS are supplementary, is Q obtuse,
acute, or right?
P
Q
T
R
S
5.
Find the value of x for each figure.
a.
b.
(x+4)
(2x)
(2x)
(3x)
6.
Find the measure of angle A.
A
a.
(3x)
A
b.
104
41
65
B
135
C
D
G
F
7.
Given ∆ ABC  ∆ PHL, complete the following statements:
a.  P 
60
b. BC 
c. m  L =
L
B
P
25
32
45
75
A
28
C
H
d. AC =
e. ∆ HPL 
8.
Determine whether each pair of triangles is congruent. If yes, explain
why.
a.
∆DGF  ∆
b.
D
DG  FE
GF  ED
E
G
F
X
W
WP  YP
ZP  XP
P
∆ XPY  ∆
Y
Z
c.
B   C
E   F
AF  DE
∆ABE  ∆
A
B
C
F
E
D
J
d.
GJ  IJ
GI
∆ GJH  ∆
G
H
I
9.
On the graph, draw a triangle and label the coordinates of the
vertices. Find the midpoint of two of the sides and draw a segment
connecting them. There is a geometric theorem that says that the
measure of this segment is equal to half of the measure of the third
side. Prove this theorem algebraically.
10.
The coordinate grids below show three paths to get from
point A(-3,-1) to point B(2,2).
a.
b.
Path 1
Find the distance along each path. Round to hundredths.
If the grid represents streets in a city, which path would a
taxicab be least likely to take? Explain your reasoning.
Path 2
Path 3
11.
Given ∆ DAR with vertices D(2,6), A(4,-5), and R(-3,0), use the
distance formula to show that ∆ DAR is scalene.
12.
Tom and Joe are going hiking. Tom hikes from the parking lot to
Horse Rock, and Joe stays at the Parking Lot.
a.
Both hikers have portable radios that have a maximum range of
two miles. Can Tom and Joe get in contact with each other when
Tom reaches Horse Rock? Explain your answer.
b.
Later that day Joe starts hiking and meets Tom for lunch at the
halfway point between the parking lot and Horse Rock. What are
the coordinates of their grid location for lunch? Show your work.
13.
A baseball diamond is a square with 90-foot sides. What is the
approximate distance of a catcher’s throw from home plate to second
base?
14.
The following is a rule of thumb for safely positioning a ladder: The
distance from the bottom of the ladder to the wall should be onefourth of the length of the ladder. Thus, the bottom of a 16-foot
ladder should be 4 feet from the wall. How far up the wall will the
ladder reach?
15.
Which of the following best describes the triangle?
7
5
9
a.
c.
16.
b.
d.
equilateral
right
Angles 1 and 2 are supplementary. If m1 is 67, what is the measure
of 2?
a.
c.
17.
scalene
isosceles
67
113
Find the measure of 1.
a.
32
c.
35
b.
d.
b.
d.
23
123
58
55
32
35
1
18.
In which of the following figures are 1 and 2 vertical angles?
a.
b.
2
1
c.
1
d.
1
In which of the following figures are 1 and 2 a linear pair?
a.
b.
c.
1
2
1
d.
1
2
20.
1
2
2
19.
2
2
1
2
In which of the following figures are 1 and 2 complementary
angles?
a.
b.
1
1
2
c.
d.
1
2
1
2
2
21.
In which of the following figures are 1 and 2 supplementary angles?
a.
b.
1
c.
2
1
d.
1
1
2
2
22.
2
Given ∆ABC and ∆ADC with AB  AD and BAC  DAC, determine
which postulate can be used to verify that ∆ABC  ∆ADC.
B
A
C
D
a.
c.
ASA
SSS
b.
d.
SAS
SSA