Download Practice worksheet - EDUC509B

Name
LESSON
7-3
Date
Class
Practice A
Triangle Similarity: AA, SSS, SAS
Fill in the blanks to complete each postulate or theorem.
to the three sides of
1. If the three sides of one triangle are
another triangle, then the triangles are similar.
2. If two sides of one triangle are proportional to two sides of another triangle and their
.
included angles are congruent, then the triangles are
to two angles of another
3. If two angles of one triangle are
triangle, then the triangles are similar.
Name two pairs of congruent angles in Exercises 4 and 5 to show that
the triangles are similar by the Angle-Angle (AA) Similarity Postulate.
4.
!
5.
8
37°
4
$
37°
:
"
9
#
5
6
&
%
Substitute side lengths into the ratios in Exercise 6. If the ratios are equal,
the triangles are similar by the Side-Side-Side (SSS) Similarity Theorem.
6.
12
' 6
12 (
9
)
+
*
24
18
,
GH ___
HI ___
JK
GI ___
KL
JL
Name one pair of congruent angles and substitute side lengths into
the ratios in Exercise 7. If the ratios are equal and the congruent
angles are in between the proportional sides, the triangles are similar
by the Side-Angle-Side (SAS) Similarity Theorem.
7.
0
5
8
1
20
4
10
16
2
congruent angles:
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
3
PQ ___
ST
19
QR ___
TU
Holt Geometry
LESSON
7-3
Practice A
LESSON
7-3
Triangle Similarity: AA, SSS, SAS
Fill in the blanks to complete each postulate or theorem.
proportional
1. If the three sides of one triangle are
another triangle, then the triangles are similar.
Practice B
Triangle Similarity: AA, SSS, SAS
For Exercises 1 and 2, explain why the triangles are similar and write
a similarity statement.
to the three sides of
1.
#
similar
included angles are congruent, then the triangles are
3. If two angles of one triangle are
triangle, then the triangles are similar.
congruent
Name two pairs of congruent angles in Exercises 4 and 5 to show that
the triangles are similar by the Angle-Angle (AA) Similarity Postulate.
4.
!
8
5.
37°
4
$
%
"
to two angles of another
37°
7
8
—
—
.
4
2.
$
!
2. If two sides of one triangle are proportional to two sides of another triangle and their
5
9
6
Possible answer: ACB and
Possible answer: Every equilateral
ECD are congruent vertical
triangle is also equiangular, so
angles. mB mD 100°,
each angle in both triangles
so B D. Thus, ABC measures 60°. Thus, TUV EDC by AA .
WXY by AA .
:
"
9
#
5
B Y; C Z
6
&
%
For Exercises 3 and 4, verify that the triangles are similar. Explain why.
F V; D T
3. JLK and JMN
4. PQR and UTS
+
6.
12
' 6
12 (
9
)
+
*
*
,
12
0
_1_
9
___
HI ___
2
5
20
8
_1_
18
KL
12
___
GI ___
2
_1_
24
JL
2
5
2
8
___
10
PQ ___
ST
_4_
5
16
___
20
QR ___
TU
Holt Geometry
TS
$
1.25
'
Holt Geometry
Review for Mastery
Triangle Similarity: AA, SSS, and SAS
"
—
—
$
0
4
5
2
4
78°
E
Side-Side-Side (SSS)
Similarity
3 3 ; 3 3 3
C
15
18
12
10
F
A
14.4
E
ABC DEF
D
B
If two sides of one triangle
are proportional to two sides
of another triangle and
their included angles are
congruent, then the triangles
are similar.
Side-Angle-Side (SAS)
Similarity
D
12
B
If the three sides of one
triangle are proportional
to the three corresponding
sides of another triangle,
then the triangles are similar.
C
15
57°
57°
12
10
18
F
A
E
ABC DEF
3
1
_ _ _
Possible answer: Draw diagonals HK, HJ, QS,
_
and QT. G and P are right angles, so they are
Explain how you know the triangles are similar, and write a similarity statement.
)
(
*
'
+
4
3
1.
0
2 R
K
2.
U
49°
H
24
18
J
Q 92°
1
S
GH _3_, so GHK PQT by SAS. It is given that
GK ___
congruent. ___
PT
PQ 2
IJ _3_, so HIJ QRS by SAS. Because GHK
HI ___
I R. ___
QR RS 2
HJ _3_
HK _3_ and GHK PQT. Because HIJ QRS, ___
PQT, ___
QT 2
QS 2
and IHJ RQS. It is given that H Q. So by the Angle Addition
T
92°
16
39°
27
L
G
V
Q T by the Def. of . By
the Sum Thm., mS 39 and
HJG LJK by the Vert. GJ __
HJ ___
2 . GHJ Thm. ___
LJ
KJ 3
mU 49, so S V and
KLJ by SAS .
R U. QRS TUV
by AA .
HJ _3_, so KHJ TQS by SAS.
HK ___
Postulate, KHJ TQS. ___
QT QS 2
JK ___
HK _3_. All the corresponding angles are
Because KHJ TQS, ___
ST QT 2
congruent; all the corresponding sides are proportional. Thus, GHIJK 3. Verify that ABC MNP.
BC ____
CA __
4 ; ABC AB ____
____
MN
NP
PM
A
12
5
C
P
12
8
B
15
10
N
M
15
MNP by SSS .
PQRST by the definition of similar polygons.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
F
A
6
5. Use triangle similarity to prove that GHIJK PQRST.
21
57°
57°
ABC DEF
3
7
2
78° C
If two angles of one triangle
are congruent to two angles
of another triangle, then the
triangles are similar.
Angle-Angle (AA)
Similarity
#
also each have a right angle, so ABC ADB by AA . They have a
similarity ratio of _2_. ABC and BDC share C. They also each have
1
a right angle, so ABC BDC by AA . They have a similarity ratio
2 3 to 1. By the Transitive Property of Similarity, ADB BDC.
of ____
3
3 to 1.
They have a similarity ratio of ___
3
6 2 3
AD 1 and DC 3. Find the perimeter of ABC.
3. Use the similarity ratios you found in Exercise 1 and the answer
to Exercise 2 to find the perimeters of ADB and BDC.
D
B
1. Prove similarity relationships between triangles in the figure.
Give a similarity ratio for each relationship you find.
Possible answer: ABC and ADB share A. They
&
20
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
7-3
!
5
US
5
3.25
#
LESSON
Use the figure for Exercises 1–3.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
UT
right angles, so they are congruent. Thus, CDG CEF by AA .
Triangle Similarity: AA, SSS, SAS
3
Thus, PQR UTS by SSS .
Possible answer: C C by the Reflexive Property. CGD and F are
_4_
5
Practice C
4. Find ST.
Thus, JLK JMN by SAS .
QR ___
PQ ___
PR _3_.
___
DE 9.75
19
13
___
Possible answer:
5. DE
3
Q T
Possible answer: It is given that
JL _4_.
KL ___
JMN L. ___
MN JM 3
For Exercise 5, explain why the triangles are
similar and find the stated length.
4
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2.
3.5
6
,
%
10
16
congruent angles:
7-3
8
12
.
Name one pair of congruent angles and substitute side lengths into
the ratios in Exercise 7. If the ratios are equal and the congruent
angles are in between the proportional sides, the triangles are similar
by the Side-Angle-Side (SAS) Similarity Theorem.
LESSON
4
3
3
24
6
___
JK
1
2
18
GH ___
7.
24
1.8
3.6
16
-
1
2.1
0
Substitute side lengths into the ratios in Exercise 6. If the ratios are equal,
the triangles are similar by the Side-Side-Side (SSS) Similarity Theorem.
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Geometry
Holt Geometry
4/12/07 4:32:37 PM