Download Geometry 2 Unit 2

Geometry 2 Unit 2
Problem Solving with Proportions
M
Name _______________________
N
Q
L
P
MN = 6
NQ = 15
LP = 5
LM = 13
1. In the diagram
MQ = LQ
MN LP
Find the length of LQ.
2. In the diagram
LM = MQ
PN
NQ
Find the length of PN.
3. Find the geometric mean between 35 and 175.
4. You are building a scale model of your uncle’s fishing boat. The boat is 62 ft long
and 23 ft wide. The model will be 14 in long. How wide should it be?
5. The perimeter of  PQR is 48,
PQ = 18,  PQR   STU, and
ST = 24. What is the perimeter of  STU?
Geometry 2 Unit 2
Similar Polygons
Name _______________________
1. Similar polygons have angles that are __________________________.
2. Similar polygons have sides that are __________________________.
3. You have a photo 4 in wide by 6in long that you want to reduce to fit a frame that is
1.5 in wide. How long will the reduced photo be?
4. ∆UVW is similar to ∆YXW. Find the value of UW.
U
V
5
W
12
6.4
Y
X
5. What is the scale factor of the two triangles in the diagram above?
Geometry 2 Unit 2
Similar Triangles
Name _______________________
33
L
M
106°
N
20
Q
36°
30
P
In the diagram, ∆LMN ~ ∆PQN. LM || QP.
1. mM = _________
2. mP = __________
3. MN = ___________
4. QM = ___________
5. What is the scale factor of the two triangles?
Geometry 2 Unit 2
Proving Triangles are Similar
Name _______________________
1. Shown below is an illustration of the ______.
2. Which triangle is NOT similar to any of the others?
[A]
[B]
30
60
60
[C]
[D]
30
50
80
3. Find the value of x to one decimal place.
4. Which triangle is not similar to any of the others?
A.
B.
C.
45°
D.
45°
45°
Geometry 2 Unit 2
Proportions and Similar Triangles
Name _______________________
3. In the figure shown, PQ = 32
cm,
ST = 8 cm, and m  QRP = 70 .
Find m S .
1. Given AE || BD . Solve for x.
A
x
B
E
4
D
P
9
Q
C
6
R
T
S
m S =
2. Given that ABC ~ DEF , solve for
x and y.
4. Given: PQ || BC . Find the length of
AP .
A
A
x
P
D
12
y
x
6
B
x = _____
7
C
E
y = ____
4
8
6
Q
12
F
B
C
Geometry 2 Unit 2
Proportions and Similar Triangles
Name _______________________
1. Two ladders are leaning against a
wall at the same angle as shown. How
long is the shorter ladder?
3. A building casts a shadow 216 meters
long. At the same time, a pole 3 meters
high casts a shadow 6 meters long. What
is the height of the building? (hint:
sketch it out)
40 ft
30 ft
12 ft
2. Janet, who is 2 meters tall, wants to
find the height of a tree in her backyard.
From the tree’s base, she walks 8 meters
along the tree’s shadow to a position
where the end of her shadow exactly
overlaps the end of the tree’s shadow.
She is now 5 meters from the end of the
shadows. How tall is the tree?
6
.
1
0
1
.
8
2
1
2.
2
0