Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 7 Corrective #1 1516
Matching
Match each vocabulary term with its definition.
a. dilation
b. indirect measurement
c. transformation
d. translation
e. scale factor
f. similarity ratio
g. scale drawing
h. scale
____
1. the ratio of two corresponding linear measurements in a pair of similar figures
____
2. in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the
preimage
____
3. the ratio of any length in a drawing to the corresponding actual length
____
4. a drawing that uses a scale to represent an object as smaller or larger than the original object
____
5. a method of measuring an object by using formulas, similar figures, and/or proportions
____
6. a transformation in which the lines connecting every point P with its preimage P ′all intersect at a point C,
CP ′
and
is the same for every point P, or a transformation that changes the size of a figure but not its shape
CP
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
7. Prove that circle A with center (–1, 5) and radius 4 is similar to circle B with center (–4, 3) and radius 2.
a. Circle A can be mapped to circle A’ by a translation (x,y) → (x − 2,y − 3). Then circle A’
1
can be mapped to circle B by a dilation with scale factor .
2
So, circles A and B are similar.
b. Circle A can be mapped to circle A’ by a translation (x,y) → (x − 2,y − 3). Then circle A’
can be mapped to circle B by a dilation with scale factor 2.
So, circles A and B are similar.
c. Circle A can be mapped to circle A’ by a translation (x,y) → (x − 3,y − 2). Then circle A’
1
can be mapped to circle B by a dilation with scale factor .
2
So, circles A and B are similar.
d. Circle A can be mapped to circle A’ by a translation (x,y) → (x − 3,y − 2). Then circle A’
can be mapped to circle B by a dilation with scale factor 2.
So, circles A and B are similar.
1
Name: ________________________
____
ID: A
8. Identify the pairs of congruent angles and corresponding sides.
a.
∠B ≅ ∠D, ∠C ≅ ∠E , ∠A ≅ ∠F ,
b.
∠B ≅ ∠D, ∠C ≅ ∠E , ∠A ≅ ∠F ,
AB BC
3
AC
=
=
=
EF
DF DE 4
∠B ≅ ∠D, ∠C ≅ ∠E , ∠A ≅ ∠F ,
EF DF DE 1
=
=
=
AB AC BC
2
∠B ≅ ∠D, ∠C ≅ ∠E , ∠A ≅ ∠F ,
AC DF DE 4
=
=
=
EF
AB BC
3
c.
d.
EF
DF DE 3
=
=
=
AC
AB BC
4
Short Answer
9. A model airplane is built to a scale of 1 in.:12 ft. If the model plane is 11 inches long, find the length of the
actual plane, rounded to the nearest foot.
10. PQ with endpoints P(3,2) and Q(12,14) is dilated by a scale factor of 7. Find the length of P' Q' .
2
Name: ________________________
ID: A
11. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width
to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27"
TV screen? Round your answers to the nearest tenth of an inch.
12. To find out how wide a river is, Jon and Sally mark an X at the spot directly across from a big rock on the
other side of the river. Then they walk in a straight line along the river, perpendicular to the straight line
between the X and the rock. After walking for 20 feet Jon stops while Sally continues along the straight line
for another 10 feet. Then she makes a 90 degree turn and walks for 30 feet. When she stops and looks at the
rock she sees that the straight line from her to the rock passes through Jon. What is the distance from X to the
rock?
1
Name: ________________________
ID: A
13. Find BD .
4
ID: A
Geometry - Chapter 7 Corrective #1 1516
Answer Section
MATCHING
1.
2.
3.
4.
5.
6.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
F
E
H
G
B
A
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
7-1 Ratios in Similar Polygons
7-6 Dilations and Similarity in the Coordinate Plane
7-5 Using Proportional Relationships
7-5 Using Proportional Relationships
7-5 Using Proportional Relationships
7-6 Dilations and Similarity in the Coordinate Plane
MULTIPLE CHOICE
7. ANS: C
8. ANS: A
TOP: 7-2 Similarity and Transformations
TOP: 7-1 Ratios in Similar Polygons
SHORT ANSWER
9. ANS:
132 feet
TOP: 7-5 Using Proportional Relationships
10. ANS:
105
TOP: 7-6 Dilations and Similarity in the Coordinate Plane
11. ANS:
width: 21.6 in., height: 16.2 in.
TOP: 7-3-Ext Proving the Pythagorean Theorem
12. ANS:
60 feet
TOP: 7-3 Triangle Similarity: AA, SSS, and SAS
13. ANS:
BD = 12
TOP: 7-4 Applying Properties of Similar Triangles
1