Download Review -- Chapter 7

Review -- Chapter 7
Multiple Choice
____
1. A baseball player made six hits in nine innings. What is the ratio of hits to innings?
a. 2:3
b. 3:2
____
____
c. 2:5
d. 5:2
2. Solve the proportion to find the value of x:
a.
 17
c.
7
10
b.
10
7
d.
3
3
17
C
a.
b.
because the corresponding angles are congruent.
is not similar to
because the corresponding angles
are not congruent.
c.
because the ratio of the corresponding sides is
proportional and the corresponding angles are congruent.
d.
is not similar to
because the ratio of the corresponding
sides is not proportional.
D
C
a.
b.
c.
d.
5.9
71° 3.5
41°
B
55°
7.3
5. Find x and the measure of AB. Show your work.
a.
b.
c.
d.
A
40
10
E
12
x
56°
40°
F
4. The triangle shown below are similar. Write a similarity statement and find the value of x.
D
____
71°
27.14
E
____
A
16.1
3. Determine if the triangles are similar. Justify your answer.
F
B
33.58
____
____
6. Find x and the measures of EB and ED. Show your work.
a.
c.
b.
d.
7. Find x and the measure of AS. Show your work
a.
b.
____
c.
d.
8. Find the length of
if
and
is a midsegment of
y
7
6
E
A
5
4
3
2
(–1.5, 1.5) D
–7
–6
–5
–4
–3
–2
B (2, 1.5)
1
–1
–1
1
2
3
4
5
6
7
x
–2
–3
a. 12.25
b. 7
C
c. 49
d.
12.25
. Show your work.
____
9. Find the perimeter of the given triangle
by using the following information:
Show your work.
P
9
8
S
T
10
a. 40.5
b. 18
____
c.
d.
45
50.625
Q
10. Find PS if :
15
R
A
P
is an altitude of
is an altitude of
12
Show your work.
10
16
Q
B
a. 7.5
b. 19.2
c.
d.
D
S
R
C
4.62
19.5
____ 11. The figure below shows nested right isosceles triangles such as that the vertices of each smaller triangle are the
midpoints of the sides of the next larger triangle. If AB = 12, find HI.
a.
b.
c.
d.
3
e.
____ 12. In the figure below,
a. 10
____ 13. In
a.
b.
below, if
b. 8
is similar to
c.
. What is the length of
d.
12
? Show your work.
e.
, find the measure of AB. Show your work.
c.
d.
e.
5
Short Answer
14. Determine whether the pair of triangles is similar. Justify your answer and show your work.
15. Given
||
a). Identify the similar triangles. Write a similarity statement.
A
b). Find the value of x. Show your work.
2x - 14
c) Find the measures of sides
and
.
B
x-5
7
D
E
C
17
16. A class of 36 students has male and female students in the ratio of 4:5.
What is the number of male students in the class? Show your work.
.
17. Find x and y. Show your work.
3 x– 6
15 +2 x
2y
(2/5) y + 3
18. In the coordinate plane below, AB and CD are parallel and OC = 2OA.
How long is AB? Show your work.
B
32
A
D
0
-24
C
19. a) Identify the similar triangles using a similarity statement.
b) Find the value of x. Show your work.
c) Find the measures of sides
20. The base and height of similar triangles are shown in the table below.
Base
6
9
18
24
Height
10
15
30
40
a) Circle all of the following triangles that are similar to the triangles listed in the table. Show your work.
21
35
6
20
50
4
12
15
35
30
b) Draw 3 more triangles that are similar to the triangles in the table:
c) What is the ratio of the base to the height for the triangles in the table?
Review -- Chapter 7
Answer Section
MULTIPLE CHOICE
1. ANS: A
How many hits does the player have? How many innings did the player play? Simplify the ratio.
Feedback
A
B
C
D
Correct!
This is the ratio of innings to hits.
Do not add the number of innings and hits.
How many innings are in the game?
PTS: 1
DIF: Basic
REF: Lesson 7-1
OBJ: 7-1.1 Write ratios.
STA: G.9(B)
TOP: Write ratios. KEY: Ratios
2. ANS: D
Find the cross products. Multiply. Divide each side by the coefficient of the variable.
Feedback
A
B
C
D
Reverse the numerator and denominator.
Check your cross multiplication.
The left side of the proportion cannot be reduced before cross multiplying.
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-1
OBJ: 7-1.2 Use properties of proportions.
STA: G.9(B)
TOP: Use properties of proportions.
KEY: Proportions
3. ANS: B
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
Feedback
A
B
C
D
In order for the triangles to be similar, the corresponding angles must be congruent and
the ratio of corresponding sides must be proportional.
Correct!
Are the angles congruent?
Check the ratio of the corresponding sides.
PTS:
STA:
KEY:
4. ANS:
1
DIF: Basic
REF: Lesson 7-2
G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B)
Similar Figures
B
OBJ: 7-2.1 Identify similar figures.
TOP: Identify similar figures.
Feedback
A
B
C
D
Is AC the same length as EF?
Correct!
Check the ratio of the corresponding sides.
Check the similarity statement.
PTS: 1
DIF: Basic
REF: Lesson 7-3
OBJ: 7-3.1 Identify similar triangles.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C)
TOP: Identify similar triangles.
KEY: Similar Triangles
5. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Correct!
Which side is AB?
Check your operations.
Which side does the question ask you to find?
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C)
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
6. ANS: D
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
C
D
Check your ratio.
Check your ratio and the values of the triangle sides.
Check the expressions for each side of the triangle.
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C)
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
7. ANS: A
Determine the ratio of corresponding parts. Use the ratio to find the missing information.
Feedback
A
B
Correct!
Check your ratios.
C
D
Check your ratios.
Which side is missing?
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.2 Use similar triangles to solve problems.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C)
TOP: Use similar triangles to solve problems.
KEY: Similar Triangles | Solve Problems
8. ANS: B
A midsegment of a triangle is one-half the length of the third side.
Feedback
A
B
C
D
What is the distance formula?
Correct!
Remember to take the square root.
This is the length of BD not AE.
PTS: 1
DIF: Average
REF: Lesson 7-4
OBJ: 7-4.2 Divide a segment into parts.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B)
TOP: Divide a segment into parts.
KEY: Lines Segments | Divide Line Segments
9. ANS: A
If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides.
Feedback
A
B
C
D
Correct!
Interchange the numerator and the denominator on either side of the proportion.
If two triangles are similar, then the perimeters are proportional to the measures of the
corresponding sides.
Check your proportion again.
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.1 Recognize and use proportional relationships of corresponding perimeters of similar triangles.
TOP: Recognize and use proportional relationships of corresponding perimeters of similar triangles.
10. ANS: A
If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the
corresponding sides.
Feedback
A
B
C
D
Correct!
Interchange the numerator and the denominator on either side of the proportion.
Use the correct proportion.
If two triangles are similar, then the measures of the corresponding altitudes are
proportional to the measures of the corresponding sides.
PTS: 1
DIF: Basic
REF: Lesson 7-5
OBJ: 7-5.2 Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians
of similar triangles.
TOP: Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of
similar triangles.
11. ANS: C
PTS: 1
TOP: Trigonometry
12. ANS: D
PTS: 1
TOP: Triangles and Quadrilaterals
13. ANS: A
PTS: 1
TOP: Triangles and Quadrilaterals
SHORT ANSWER
14. ANS:
Not enough information to prove similarity.
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their
corresponding sides are proportional.
PTS: 1
DIF: Average
REF: Lesson 7-3
OBJ: 7-3.1 Identify similar triangles.
STA: G.2(B) | G.3(B) | G.4 | G.9(B) | G.11(A) | G.11(B) | G.11(C)
TOP: Identify similar triangles.
KEY: Similar Triangles
15. ANS:
; AB = 7
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The measures of the corresponding sides of similar triangles are proportional.
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
16. ANS:
16
REF: Lesson 7-3
OBJ: 7-3.3 Solve multi-step problems.
REF: Lesson 7-1
OBJ: 7-1.3 Solve multi-step problems.
REF: Lesson 7-4
OBJ: 7-4.3 Solve multi-step problems.
Let x be the number of male students.
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
17. ANS:
To find x:
To find y:
PTS: 1
DIF: Basic
TOP: Solve multi-step problems.
18. ANS:
15
PTS: 1
19. ANS:
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The measures of the corresponding sides of similar triangles are proportional.
PTS: 1
DIF: Advanced
TOP: Solve multi-step problems.
REF: Lesson 7-3
OBJ: 7-3.3 Solve multi-step problems.