Download Geometry B Name Unit 4B Date Period Lesson 1 Practice Write the

Geometry B
Unit 4B
Lesson 1 Practice
Name
Date
1) Write the angles of the triangle in order
from smallest to largest.
___________________________________
Period
2) Write the sides of the triangle in order from
shortest to longest.
___________________________________
In questions 3-5, prove or disprove that the given side lengths can form a triangle.
3) 6, 9, 4
4) 3.8, 2.7, 8.9
5) 4.5, 6, 10.5
In questions 6-8, the length of two sides of a triangle are given. Find the range of possible lengths of
the third side.
6) 8 mm, 12 mm
7) 16 ft, 16 ft
8) 11.4 cm, 12 cm
In questions 9-11, determine if the triangle with the given side lengths is acute, right, or obtuse. Show
work to support your answer.
9) 7, 10, 12
10) 9, 11, 15
11) 9, 40, 41
12) List the side lengths in order from shortest to longest. (Hint: Use the Triangle Sum Theorem to find
the angles in the triangle.)
13) The five steel tubes of this mountain bike frame form two triangles. List
the five tubes in order from shortest to longest.
In questions 14-16, use the Pythagorean Theorem to find the missing side in each triangle. Round to the
nearest tenth, if necessary.
15)
14)
16)
17) Fill in the blanks in order to find the missing sides of the triangle by Pythagorean Theorem.
a2  b2  c 2
72  x 2  
x2 


2

 x 2  x 2  x  x 1
x2 x2 
x2

1
x
x+1
x2
1

24  x
What are the three side lengths?
7
Geometry B
Unit 4B
Lesson 2 Practice
1) If 2x  5 y , then
Given that
2)
b

a
Name
Date
x

y
a 5
 , complete each equation.
b 7
a
Solve each proportion.
x 40
5)

2 16
8)
4
12

3x 7x  6
Period
3)
6)
9)
5
9
x
x
7
4) 7a 


4
13
7)
3 10

5 x

2x  1
17.5
10)
5
4x  1

6 2x  10
11) The ratio of boys to girls taking Geometry is 27 : 31 . If 346 students are enrolled in Geometry this
year, approximately how many of them are boys and approximately how many of them are girls?
12) The ratio of the side lengths in a quadrilateral is 2 : 4 : 5 : 7 , and the perimeter is 135 cm. Find the
lengths of each side.
13) The ratio of the angle measures in a triangle is 5 : 12 : 19 . Find the measure of each angle in the
triangle.
14) Jenny is 5 feet 2 in tall. To find the height of a light pole, she measured her shadow and the pole’s
shadow. What is the height of the pole?
15) To find the height of a dinosaur in a museum, Timmy placed a mirror on the ground 40 feet from its
base. Then, he stepped back 4 feet so that he could see the top of the dinosaur in the mirror. Timmy’s
eyes were approximately 5 ft 6 in above the ground. What is the height of the dinosaur?
16) The town of Goodland, Kansas, claims that it
has one of the world’s largest easels. It holds
an enlargement of a van Gogh painting that
is 24 feet wide. The original painting is 58 cm
wide and 73 cm tall. If the reproduction is
similar to the original, what is the height of
the reproduction to the nearest foot?
17) The photo shows a person who is 5 feet 1 in
tall standing by a statue in Jamestown, North
Dakota. Estimate the actual height of the
statue by using a ruler to measure the ratio
of her height and the height of the statue in
the photo.
Geometry B
Unit 4B
Lesson 3 Practice
Name
Date
Period
For questions 1-4, determine if each pair of figures is similar to each other.
If so, identify the corresponding sides and angles and determine the similarity ratio and complete the
similarity statement. If not, explain why they are not similar.
1)
Similarity Statement: ABCD ~ ____________________
Scale Factor
2)
List Congruent Angles
Similarity Statement: JKLM ~ ____________________
Scale Factor
3)
Similarity ratio
Similarity ratio
List Congruent Angles
Similarity Statement: QRS ~ ____________________
Scale Factor
List Proportional Sides
List Proportional Sides
Similarity ratio
List Congruent Angles
List Proportional Sides
4)
Similarity Statement: ABCD ~ ____________________
Scale Factor
5)
Given that ABCD ~ EFGH, complete the
problem to find the value of x.
AB EF

BC
4
x 3

3
4  2x  4   3  x  3 
Similarity ratio
List Congruent Angles
6)
List Proportional Sides
Given that MNP
XYZ , complete the
problem to find the value of x.
MP

NP YZ

Geometry B
Unit 4B
Lesson 4 Practice
Name
Date
Prove or explain why the triangles are similar and write a similarity statement.
1)
Similarity Statement: ____________________ ~ ____________________
2)
Similarity Statement: ____________________ ~ ____________________
3)
Similarity Statement: ____________________ ~ ____________________
4)
Similarity Statement: ____________________ ~ ____________________
5)
Similarity Statement: ____________________ ~ ____________________
Period
6)
Explain why AED
ACB .
Find DB.
7)
Explain why triangles EFG and HJG are similar.
Mark / color the corresponding parts of similar triangles EFG and HJG.
Find the value of x.
Geometry B
Unit 4B
Lesson 5 Practice
Name
Date
Period
1)
Find DG. Show work and provide a theorem that verifies your answer.
2)
Find RN. Show work and provide a theorem that verifies your answer.
3)
Is TU RS ? Show work and provide a theorem that verifies your answer.
4)
The map shows the area around Herald Square in Manhattan, NY, and approximate length of several
streets. If the numbered streets are parallel, what is the length of Broadway between 34th St. and 35th
St.? Round to the nearest foot.
5)
Find QR and RS.
6)
Find CD and AD. Show work and provide a theorem that verifies your answer.
7)
In the figure BC DE FG . Complete each proportion.
8)
A developer is laying out lots along Grant Rd. whose total width is 500 feet. Given the width of each
lot along Chavez St., what is the width of each of the lots along Grant Rd, Round to the nearest foot.
Geometry B
Unit 4B
Lesson 6 Practice
1) In each question,
the blanks.
a. k = 2,
Name
Date
Period
ABC ~ DEF , with the given scale factor. DEF is bigger than ABC . Fill in
ABC : Perimeter = 12 in; Area = 36 in2
DEF : Perimeter = ______; Area = _______
b. k = 3.5,
ABC : Perimeter = 4 cm; Area = 10.5 cm2
DEF : Perimeter = ______; Area = _______
c. k = 6,
ABC : Perimeter = ______; Area = _______
DEF : Perimeter = 12 in ; Area = 180 in2
d. k = 4,
ABC : Perimeter = 10 in; Area = _______
DEF : Perimeter = ______; Area = 96 in2
2) Given that rectangle MNPQ ~ RSTU, find the following.
a. Find the perimeter of RSTU.
b. Find the area of RSTU.
3) Given that pentagon ABCDE ~ FGHJK, find the following.
a. Find the perimeter of FGHJK.
b. Find the area of FGHJK.
4)
Given that rectangle ABCD ~ EFGH, the area of rectangle ABCD is 135 in2 and the area of rectangle
EFGH is 240 in2. If the width of rectangle ABCD is 9 in, what is the length and width of rectangle
EFGH?