7-3 Similar Triangles: AA Similarity
Determine whether the triangles are similar,
using the AA Similarity Theorem. If so, write a
similarity statement.
3.
1.
SOLUTION:
Since
and both are right
angles, or 90°. By the Triangle Sum Theorem, 90 +
38 +
= 180, so
. Since
. So, the angles are not
congruent.
SOLUTION:
∠XYZ ≅ ∠WVZ by the Vertical Angles Theorem.
Since
, ∠X ≅ ∠W.
So, △YXZ ∼ △VWZ by AA Similarity.
ANSWER:
Yes;
ANSWER:
by AA Similarity.
No; the angles are not congruent.
2.
SOLUTION:
Since
and both are right
angles, or 90°. By the Triangle Sum Theorem, 90 +
49 +
= 180, so
. Since
. So, △ABC ∼ △FED by AA
Similarity.
ANSWER:
Yes; △ABC ∼ △FED by AA Similarity.
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4.
SOLUTION:
It is given that two of the angles are congruent, so
the remaining angles must also be congruent. So,
△ABC ∼ △FED by AA Similarity.
ANSWER:
Yes; △ABC ∼ △FED by AA Similarity.
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7-3 Similar Triangles: AA Similarity
5. MULTIPLE CHOICE In the figure,
intersects
at point C.
Which additional information would be enough to
prove that
A
DAC and
B
and
C
D
ECB are congruent.
STRUCTURE Identify the similar triangles.
Find each measure.
6. XZ
SOLUTION:
By AA Similarity,
Use the corresponding side lengths to write a
proportion.
are congruent.
and
are parallel.
CBE is a right angle.
SOLUTION:
Since
, by the Vertical Angle
Theorem, option C is the best choice. If we know
that
, then we know that the alternate
interior angles formed by these segments and sides
and
are congruent. This would allow us to
use AA Similarity to prove the triangles are similar.
Solve for y.
ANSWER:
△XYZ ∼ △JKL; 4
ANSWER:
C
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7-3 Similar Triangles: AA Similarity
7. VS
SOLUTION:
We can see that
because all right
triangles are congruent.
Additionally,
, by Reflexive Property.
Therefore, by AA Similarity,
.
Use the corresponding side lengths to write a
proportion.
Solve for x.
ANSWER:
8. COMMUNICATION A cell phone tower casts a
100-foot shadow. At the same time, a 4-foot 6-inch
post near the tower casts a shadow of 3 feet 4
inches. Find the height of the tower.
SOLUTION:
Make a sketch of the situation. 4 feet 6 inches is
equivalent to 4.5 feet.
In shadow problems, you can assume that the angles
formed by the sun’s rays with any two objects are
congruent and that the two objects form the sides of
two right triangles.
Since two pairs of angles are congruent, the right
triangles are similar by the AA Similarity Postulate.
So, the following proportion can be written:
Let x be the tower’s height. (Note that 1 foot = 12
inches and covert all the dimensions to inches)
100 ft = 1200 inches
4 feet 6 inches = 54 inches
3 feet 4 inches = 40 inches.
Substitute these corresponding values in the
proportion.
So, the cell phone tower is 1620 inches or 135 feet
tall.
ANSWER:
135 ft
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7-3 Similar Triangles: AA Similarity
Determine whether the triangles are similar. If
so, write a similarity statement. Explain your
reasoning.
9. △ACE, △BCD
11.
SOLUTION:
It is given that two of the angles are congruent, so
the remaining angles must also be congruent. So,
△TUV ∼ △VXW by AA Similarity.
SOLUTION:
ANSWER:
△ACE ∼ △BCD by AA Similarity. It is given that
one angle is 57°, which can be used to find that the
other angles are 57° and 66°, respectively. These
measure hold true for each triangle, and thus the
larger triangle as well.
Yes; △TUV ∼ △VXW by AA Similarity.
Determine whether the triangles are similar. If
so, write a similarity statement. Explain your
reasoning.
ANSWER:
Yes; △ACE ∼ △BCD by AA Similarity.
12.
10.
SOLUTION:
No;
needs to be parallel to
for
by AA Similarity. Additionally, there
are no given side lengths to compare to use SAS or
SSS Similarity theorems.
SOLUTION:
We know that
due to the Reflexive
property. Additionally, we can prove that
, because they are corresponding
angles formed by parallel lines . Therefore,
by AA Similarity.
ANSWER:
Yes;
by AA Similarity.
ANSWER:
No;
needs to be parallel to
by AA Similarity.
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Page 4
7-3 Similar Triangles: AA Similarity
15. MODELING Scientists are studying eyes and how
13.
SOLUTION:
There is not enough information given to determine
that the triangles are similar.
light is refracted by the lens of the eyes to create
two similar triangles. Prove that the triangles are
similar using similarity transformations and the
relationship between the angles and sides of the
triangles.
ANSWER:
No; not enough information is given to determine
that the triangles are similar.
SOLUTION:
You can reflect or rotate one triangle about the
shared vertex B, then dilate one triangle to show the
triangles are similar.
ANSWER:
14.
SOLUTION:
No; the angles of
are 59, 47, and 74 degrees
and the angles of
are 47, 68, and 65 degrees.
Since the angles of these triangles won't ever be
congruent, so the triangles can never be similar.
Reflect or rotate one triangle about the shared
vertex B, then dilate one triangle to show the
triangles are similar.
ANSWER:
No; the angles of the triangles are not congruent, so
the triangles are not similar.
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7-3 Similar Triangles: AA Similarity
ALGEBRA Identify the similar triangles. Then
find each measure.
16. EG
17. ST
SOLUTION:
By the Reflexive Property, we know that
.
.
Also, since
, we know that
( Corresponding Angle Postulate).
SOLUTION:
We are given one pair of congruent angles, and we
know that
by the Vertical Angles
Theorem. So, we know that △DEC ∼ △GEF by AA
Similarity.
Therefore, by AA Similarity,
Use the corresponding side lengths to write a
proportion.
Use the corresponding side lengths to write a
proportion.
Solve for x.
Solve for x.
ANSWER:
△DEC ∼ △GEF; 4
ANSWER:
18. WZ, UZ
SOLUTION:
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7-3 Similar Triangles: AA Similarity
We are given that
know that
congruent.)
and we also
( All right angles are
19. HJ, HK
Therefore, by AA Similarity,
Use the Pythagorean Theorem to find WU.
SOLUTION:
Since we are given two pairs of congruent angles, we
know that
, by AA Similarity.
Use the corresponding side lengths to write a
proportion.
Since the length must be positive, WU = 24.
Use the corresponding side lengths to write a
proportion.
Solve for x.
Solve for x.
Substitute x = 2 in HJ and HK.
HJ = 4(2) + 7
=15
HK = 6(2) – 2
= 10
Substitute x = 12 in WZ and UZ.
WZ = 3x – 6
=3(12) – 6
= 30
UZ = x + 6
= 12 + 6
= 18
ANSWER:
ANSWER:
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7-3 Similar Triangles: AA Similarity
20. EB
SOLUTION:
We are given that each triangle has a right angle, and
using the Triangle Sum Theorem we can determine
that
. Because both triangles have angle
measures of 90°, 36°, and 54°, we know that △ABE
∼ △DCE by AA Similarity.
21. GD, DH
SOLUTION:
We know that
are given
Therefore,
( Reflexive Property) and
.
by AA Similarity.
Use the corresponding side lengths to write a
proportion:
Use the corresponding side lengths to write a
proportion.
Solve for x.
Solve for x.
ANSWER:
△ABE ∼ △DCE; 6
Substitute x = 8 in GD and DH.
GD = 2 (8) – 2
= 14
DH = 2 (8) + 4
= 20
ANSWER:
22. STATUES Mei is standing next to a statue in the
park. If Mei is 5 feet tall, her shadow is 3 feet long,
and the statue’s shadow is
feet long, how tall is
the statue?
SOLUTION:
Make a sketch of the situation. 4 feet 6 inches is
equivalent to 4.5 feet.
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7-3 Similar Triangles: AA Similarity
equivalent to 4.5 feet.
In shadow problems, you can assume that the angles
formed by the Sun’s rays with any two objects are
congruent and that the two objects form the sides of
two right triangles.
Since two pairs of angles are congruent, the right
triangles are similar by the AA Similarity Postulate.
So, the following proportion can be written:
In shadow problems, you can assume that the angles
formed by the Sun’s rays with any two objects are
congruent and that the two objects form the sides of
two right triangles.
Since two pairs of angles are congruent, the right
triangles are similar by the AA Similarity Postulate.
So, the following proportion can be written:
Let x be the statue’s height and substitute given
values into the proportion:
Let x be the basketball goal’s height. We know that 1
ft = 12 in.. Convert the given values to inches.
So, the statue's height is 17.5 feet tall.
ANSWER:
Substitute.
23. SPORTS When Alonzo, who is
tall, stands
next to a basketball goal, his shadow is
long, and
the basketball goal’s shadow is
long. About how
tall is the basketball goal?
SOLUTION:
Make a sketch of the situation. 4 feet 6 inches is
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ANSWER:
about 12.8 ft
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7-3 Similar Triangles: AA Similarity
24. BIRDWATCHING Taylor sees the nest of a rare
bird near the top of a tree. He wants to report its
position to the local conservation group. Taylor is 6
feet tall and casts a 3.5-foot shadow. The tree with
the nest casts a shadow 6 feet long. About how far
above the ground is the nest?
SOLUTION:
Make a sketch of the situation.
In shadow problems, you can assume that the angles
formed by the Sun’s rays with any two objects are
congruent and that the two objects form the sides of
two right triangles.
Since two pairs of angles are congruent, the right
triangles are similar by the AA Similarity Postulate.
So, the following proportion can be written:
Let x be the tree’s height. We know that 1 ft = 12 in..
Convert the given values to inches.
ANSWER:
about 10.3 feet
25. PROOF Write a two-column proof for each part of
Theorem 7.2.
SOLUTION:
Reflexive Property of Similarity
Given: △ABC
Prove: △ABC ∼ △ABC
Proof:
Statements (Reasons)
1. △ABC (Given)
2. ∠A ≅ ∠A, ∠B ≅ ∠B (Refl. Prop.)
3. △ABC ∼ △ABC (AA Similarity)
Symmetric Property of Similarity
Given: △ABC ∼ △DEF
Prove: △DEF ∼ △ABC
Proof:
Statements (Reasons)
1. △ABC ∼ △DEF (Given)
2. ∠A ≅ ∠D, ∠B ≅ ∠E (Def. of ∼ polygons)
3. ∠D ≅ ∠A, ∠E ≅ ∠B (Symm. Prop.)
4. △DEF ∼ △ABC (AA Similarity)
Transitive Property of Similarity
Given: △ABC ∼ △DEF and △DEF ∼ △GHI
Prove: △ABC ∼ △GHI
Substitute.
Proof:
Statements (Reasons)
1. △ABC ∼ △DEF, △DEF ∼ △GHI (Given)
2. ∠A ≅ ∠D, ∠B ≅ ∠E, ∠D ≅ ∠G, ∠E ≅ ∠H
(Def. of ∼ polygons)
3. ∠A ≅ ∠G, ∠B ≅ ∠H (Trans. Prop.)
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7-3 Similar Triangles: AA Similarity
4. △ABC ∼ △GHI (AA Similarity)
ANSWER:
PROOF Write a two-column proof.
26. Given: ABCD is a trapezoid.
Prove:
Reflexive Property of Similarity
Given: △ABC
Prove: △ABC ∼ △ABC
Proof:
Statements (Reasons)
1. △ABC (Given)
2. ∠A ≅ ∠A, ∠B ≅ ∠B (Refl. Prop.)
3. △ABC ∼ △ABC (AA Similarity)
SOLUTION:
Proof:
Statements (Reasons)
1. ABCD is a trapezoid. (Given)
2.
3.
Thm.)
4.
5.
(Def. of trap.)
(Alt. Int. ∠
(AA Similarity)
(Corr. sides of ~ △s are proportional.)
Symmetric Property of Similarity
Given: △ABC ∼ △DEF
Prove: △DEF ∼ △ABC
ANSWER:
Proof:
Statements (Reasons)
1. ABCD is a trapezoid. (Given)
Proof:
Statements (Reasons)
1. △ABC ∼ △DEF (Given)
2. ∠A ≅ ∠D, ∠B ≅ ∠E (Def. of ∼ polygons)
3. ∠D ≅ ∠A, ∠E ≅ ∠B (Symm. Prop.)
4. △DEF ∼ △ABC (AA Similarity)
2.
3.
Thm.)
4.
5.
(Def. of trap.)
(Alt. Int. ∠
(AA Similarity)
(Corr. sides of ~ △s are proportional.)
Transitive Property of Similarity
Given: △ABC ∼ △DEF and △DEF ∼ △GHI
Prove: △ABC ∼ △GHI
Proof:
Statements (Reasons)
1. △ABC ∼ △DEF, △DEF ∼ △GHI (Given)
2. ∠A ≅ ∠D, ∠B ≅ ∠E, ∠D ≅ ∠G, ∠E ≅ ∠H
(Def. of ∼ polygons)
3. ∠A ≅ ∠G, ∠B ≅ ∠H (Trans. Prop.)
4. △ABC ∼ △GHI (AA Similarity)
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7-3 Similar Triangles: AA Similarity
27. Given: △XYZ and △ABC are right triangles; ∠Z
= ∠C.
Prove: △YXZ ∼ △BAC
SOLUTION:
Proof:
Statements (Reasons)
1.
and
are right triangles. (Given)
2.
and
are right angles. (Def. of rt.
)
3.
(All rt. angles are .)
4. ∠Z = ∠C (Given)
5.
(AA Similarity)
ANSWER:
Proof:
Statements (Reasons)
1.
and
are right triangles. (Given)
2.
and
are right angles. (Def. of rt.
)
3.
(All rt. angles are .)
4. ∠Z = ∠C (Given)
5.
(AA Similarity)
28. Graph the triangles, and prove that
SOLUTION:
slope of
slope of
or undefined
or undefined
XZ || WV because they have the same slope. Thus,
∠YXZ ≅ ∠YWV and ∠YZX ≅ ∠YVW by the
Corresponding Angles Postulate. Therefore △XYZ
∼ △WYV by AA Similarity.
ANSWER:
COORDINATE GEOMETRY
and
have vertices X(–1, –9), Y(5, 3), Z(–1,
6), W(1, –5), and V(1, 5).
slope of
slope of
or undefined
or undefined
XZ || WV because they have the same slope. Thus,
∠YXZ ≅ ∠YWV and ∠YZX ≅ ∠YVW by the
Corresponding Angles Postulate. Therefore △XYZ
∼ △WYV by AA Similarity.
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7-3 Similar Triangles: AA Similarity
29. Find the ratio of the perimeters of the two triangles.
SOLUTION:
The lengths of the sides of
are:
XY =
YZ =
30. MODELING When Luis’s dad threw a bounce pass
to him, the angles formed by the basketball’s path
were congruent. The ball landed of the way
between them before it bounced back up. If Luis’s
dad released the ball 40 inches above the floor, at
what height did Luis catch the ball?
ZX = 6 – (–9) = 15;
The lengths of the sides of
VW = 5 – (–5) = 10;
are:
WY =
YV =
Now, find the perimeter of each triangle:
SOLUTION:
Since the ball landed of the way between them, the
horizontal line is in the ratio of 2:1.
By AA Similarity, the given two triangles are similar.
Form a proportion and solve for x. Assume that Luis
will catch the ball at a height of x inches.
ANSWER:
So, Luis will catch the ball 20 inches above the floor.
ANSWER:
20 in.
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7-3 Similar Triangles: AA Similarity
31. BILLIARDS When a ball is deflected off a smooth
surface, the angles formed by the path are congruent.
Booker hit the orange ball and it followed the path
from A to B to C as shown below. What was the total
distance traveled by the ball from the time Booker hit
it until it came to rest at the end of the table?
SOLUTION:
By AA Similarity, the given triangles are similar.
Form a proportion and solve for BC. Convert the
fractions to decimals.
32. If possible, describe a similarity transformation or a
combination of a similarity transformation and a rigid
transformation that could be used to demonstrate that
the triangles are similar.
SOLUTION:
Since the sides are in proportion, a dilation with scale
factor of 2.5 followed by a translation demonstrates
that △DEF ∼ △D′E′F′.
ANSWER:
So, the total distance traveled by the ball is about 61
inches.
ANSWER:
about 61 in.
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,
, and
, so a dilation with scale factor of
2.5 followed by a translation demonstrates that
△DEF ∼ △D′E′F′.
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7-3 Similar Triangles: AA Similarity
33. CHANGING DIMENSIONS Assume that △ABC
∼ △JKL.
a. If the lengths of the sides of △JKL are half the
lengths of the corresponding sides of △ABC, and
the perimeter of △ABC is 40 inches, what is the
perimeter of △JKL? How is the perimeter related
to the scale factor from △ABC to △JKL?
b. If the lengths of the sides of △ABC are three
times the lengths of the corresponding sides of
△JKL, and the perimeter of △ABC is 21 inches,
what is the perimeter of △JKL? How is the
perimeter related to the scale factor from △ABC to
△JKL?
SOLUTION:
a. The perimeter would be half of 40, or 20 inches.
The ratio of the perimeters is the scale factor.
b. The perimeter would be one-third of 21, or 7
inches. The ratio of the perimeters is the scale factor.
ANSWER:
a. 20 in.; The ratio of the perimeters is the scale
factor.
b. 7 in.; The ratio of the perimeters is the scale
factor.
34. MEDICINE Certain medical treatments involve
laser beams that contact and penetrate the skin.
Refer to the diagram.
b. What needs to be true for the triangles formed
by the edges of the two laser beams and the surface
of the skin to be similar to each other?
c. If all of the triangles are similar, how far apart
should the laser sources be placed to ensure that the
areas treated by each source do not overlap or
leave an area untreated?
SOLUTION:
a. The surface of the skin and the treated area
beneath the skin would need to be parallel in order for
the triangles formed to be similar.
b. The segment with endpoints at the sources would
need to be parallel to the surface of the skin in order
for the triangles formed to be similar.
c. For 100 cm, it covers an area that has a radius of
15 cm. It penetrates and go inside the skin for 5 cm.
so, the total height is 105 cm. Assume that for 105
cm, the laser source covers an area that has a radius
of x cm.
Form a proportion.
So, the laser beam covers 15.75 + 15.75 or 31.5 cm.
ANSWER:
a. The surface of the skin and the treated area
beneath the skin are parallel.
b. The segment with endpoints at the sources is
parallel to the surface of the skin.
c. 31.5 cm
a. What needs to be true for the triangles formed
by the edges of the laser beams and the surface of
the skin to be similar to triangles formed by the
edges of the laser beams and the treated area
beneath the skin?
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35. MULTIPLE REPRESENTATIONS In this
problem, you will explore proportional parts of
triangles.
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7-3 Similar Triangles: AA Similarity
formed by the ratios of sides of a triangle cut by a
parallel line.
Sample answer: The segments created by a line || to
one side of a △ and intersecting the other two sides
are proportional.
a. Geometric Draw △ABC with
parallel to
as shown.
b. Tabular Measure and record the lengths AD, DB,
CE, and EB and the ratios
and
ANSWER:
a. Sample answer:
in a table.
c. Verbal Make a conjecture about the segments
created by a line parallel to one side of a triangle and
intersecting the other two sides.
SOLUTION:
a. The triangle you draw doesn't have to be
b. Sample answer:
congruent to the one in the text. However, measure
carefully so that
is parallel to side
.
Sample answer:
c. Sample answer: The segments created by a line ||
to one side of a △ and intersecting the other two
sides are proportional.
b. When measuring the side lengths, it may be
easiest to use centimeters. Fill in the table with the
corresponding measures.
Sample answer:
c. Observe patterns you notice in the table that are
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7-3 Similar Triangles: AA Similarity
36. WRITING IN MATH Explain why the AA
Postulate requires that only two pairs of
corresponding angles rather than three are shown to
be congruent in order to prove that two triangles are
similar.
SOLUTION:
The Third Angles Theorem ensures that if two pairs
of corresponding angles in two triangles are
congruent, then the third pair of angles is also
congruent.
ANSWER:
Sample answer: The Third Angles Theorem ensures
that if two pairs of corresponding angles in two
triangles are congruent, then the third pair of angles is
also congruent.
37. CHALLENGE
is an altitude of △XYZ.
Can you prove that △WXY and △WYZ are similar
triangles? Explain.
SOLUTION:
Because
is an altitude, we know
. So
∠XWY and ∠ZWY are right angles. It is given that
∠XYZ is a right angle. Thus ∠XWY ≅ ∠XYZ and
∠XYZ ≅ ∠ZWY because all right angles are
congruent. ∠WXY ≅ ∠YXZ by the Reflexive
property. So △WXY ∼ △YXZ by AA Similarity.
∠XZY ≅ ∠YZW by the Reflexive property. So
△YXZ ∼ △WYZ by AA Similarity. Therefore △WXY
∼ △WYZ by the Transitive property.
ANSWER:
Yes; Because
is an altitude,
. So
∠XWY and ∠ZWY are right angles. It is given that
∠XYZ is a right angle. Thus ∠XWY ≅ ∠XYZ and
∠XYZ ≅ ∠ZWY because all right angles are
congruent. ∠WXY ≅ ∠YXZ by the Reflexive
property. So △WXY ∼ △YXZ by AA Similarity.
∠XZY ≅ ∠YZW by the Reflexive property. So
△YXZ ∼ △WYZ by AA Similarity. Therefore △WXY
∼ △WYZ by the Transitive property.
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7-3 Similar Triangles: AA Similarity
38. REASONING In a pair of similar triangles, the
sides of one triangle measure 3, 3.25, and 4.75 units.
The sides of the second triangle measure x – 0.46, x,
and x + 2.76 units. Find the value of x.
SOLUTION:
Using the given information, sketch two triangles and
label the corresponding sides and angles. Make sure
you use the Angle-Sides relationships of triangles to
place the shortest sides across from the smallest
angles, etc.
Form a proportion and solve for x.
39. OPEN-ENDED Draw a triangle that is similar to
△ABC shown. Explain how you know your triangle
is similar to △ABC.
SOLUTION:
When making a triangle similar to
, keep in
mind the relationships that exist between the angles
of similar triangles, as well as the sides. We know
that the corresponding sides of similar triangles are
proportional and the corresponding angles are
congruent.
ANSWER:
5.98
△A′B′C′ ∼ △ABC because the measures of each
side have a scale factor of 0.5 and the measures of
corresponding angles are equal.
ANSWER:
Sample answer:
△A′B′C′ ∼ △ABC because the measures of each
side have a scale factor of 0.5 and the measures of
corresponding angles are equal.
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7-3 Similar Triangles: AA Similarity
40. The ladder of a slide is perpendicular to the ground.
The slide slopes downward at an angle of 58 degrees.
What angles cannot be used to prove that △JKL ∼
△JMN by AA Similarity?
A
B
C
D
42. Sonia is 5 feet 6 inches tall. She wants to estimate the
height of a palm tree near her school. She measures
her shadow and the palm tree’s shadow and then sets
up the sketch shown below.
and
and
and
and
SOLUTION:
All of the pairs of angles listed are congruent by
either corresponding angles on parallel lines,
symmetry (different name for the same angle), or
because the angles at perpendicular lines except
. Those angles in answer choice C
are supplementary, but not congruent.
ANSWER:
C
41. △JKL ∼ △PQR, the measure of angle P is 34º, and
the measure of angle R is 72º. The measure of angle
K is given by the expression (7x + 32)º. What is the
value of x?
Which of the following is the best estimate of the
height of the palm tree?
A
B
C
D
28 ft
27.5 ft
13.5 ft
3.6 ft
SOLUTION:
The triangles formed are similar due to AA Similarity.
Therefore, the corresponding sides are proportional.
Set up a proportion to find the height of the tree.
Note: 6 inches is half of a foot. Therefore, 5'6" is
equivalent to 5.5 feet.
SOLUTION:
Use the Triangle Angle Sum Theorem.
34º + 72º + (7x + 32)º = 180º
138º + 7xº = 180º
7xº = 42º
x=6
The correct choice is B.
ANSWER:
B
ANSWER:
6
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7-3 Similar Triangles: AA Similarity
43. In the figure below,
44. MULTI-STEP These two triangles are similar and
.
.
a. Which proportion correctly represents the
situation?
A
a. What is the measure of angle F?
C
B
A 28º
B 68º
D
b. Find the value of x and the measure of
A
B
C
D
x = 4.4, AB = 2.4
x = 6.8, AB = 4.8
x = 9.5, AB = 7.5
x = 17, AB = 15
SOLUTION:
a. To write a true proportion, write ratios that
compare corresponding sides. Only choice D
compares corresponding sides,
b. Solve
.
.
C 74º
D 96º
b. Which of the following are true? Select all that
apply.
A
B
C
D
E
F
△EFG ∼ △RST
△EFG ∼ △TRS
△FEG is a dilation of △RTS.
△RTS is a dilation of △FEG.
SOLUTION:
a. The measure of angle F is 68º, answer B, because
it is congruent to angle R.
for x and find AB.
30 = 4x – 8
38 = 4x
9.5 = x
AB = 9.5 – 2
AB = 7.5
The correct answer is choice C.
ANSWER:
a. D
b. C
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b. Because the two triangles are similar and
, then
like in answer choice B,
because
, instead
.
To write the similarity, align corresponding angles like
in answer choice D. Since the triangles are similar,
either can be said to be a dilation of the other as long
as the corresponding angles align, so both E and F are
also true.
ANSWER:
a. B
b. B, D, E, F
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