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Name _______________________________________ Date ___________________ Class __________________
Practice A
Triangle Similarity: AA, SSS, SAS
Fill in the blanks to complete each postulate or theorem.
1. If the three sides of one triangle are ____________________ to the three sides of
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 ____________________.
3. If two angles of one triangle are ____________________ to two angles of another 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.
________________________________________
________________________________________
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.
GH


JK  
HI


KL  
GI


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.
congruent angles: 
PQ
QR
   
   
ST
TU
© Houghton Mifflin Harcourt Publishing Company
Holt McDougal Analytic Geometry
Name _______________________________________ Date ___________________ Class __________________
4. B  Y; C  Z
3. Sample answer:
5. F  V; D  T
6.
6 1 9 1 12 1
; ;
; ;
;
12 2 18 2 24 2
7. Q  T;
Problem Solving
1. Dilate the smaller triangle with a scale
factor 2 and center at the vertex of the
square border. Do the same at each
vertex of the square border.
2. He used a point of the circle as the
center of the dilation. He drew rays
outward from the center of the dilation
then enlarged the circles repeatedly.
3. Sample answer: Move one triangle onto
a coordinate plane in a convenient
position like the first quadrant. Apply
the dilation with center (0, 0) and scale
factor 2. (x, y)  (2x, 2y). The image
should then be congruent to the image
created with the graphics program.
4. Place the drawing of the smaller
rectangle on a coordinate plane in a
convenient position in the first quadrant.
Apply the dilation with center (0, 0) and
scale factor 3. (x, y)  (3x, 3y). The
image represents the larger rectangle.
5. A
6. J
Reading Strategies
1. dilation with a congruence
transformation
2. dilation
TRIANGLE SIMILARITY: AA, SSS,
AND SAS
Practice B
1. Possible answer: ACB and ECD are
congruent vertical angles. mB  mD
 100°, so B  D. Thus, ABC 
EDC by AA .
2. Possible answer: Every equilateral
triangle is also equiangular, so each
angle in both triangles measures 60°.
Thus, TUV  WXY by AA .
3. Possible answer: It is given that JMN
KL JL 4
 L.

 . Thus, JLK 
MN JM 3
JMN by SAS .
PQ QR PR 3


 .
UT TS US 5
Thus, PQR  UTS by SSS .
5. Possible answer: C  C by the
Reflexive Property. CGD and F are
right angles, so they are congruent.
Thus, CDG  CEF by AA . DE 
9.75
Practice C
1. Possible answer: ABC and ADB
share A. They also each have a right
angle, so ABC  ADB by AA .
2
They have a similarity ratio of .
1
ABC and BDC share C. They
also each have a right angle, so ABC
 BDC by AA . They have a
2 3
similarity ratio of
to 1. By the
3
Transitive Property of Similarity, ADB
 BDC. They have a similarity ratio of
3
to 1.
3
4. Possible answer:
2. 6  2 3
Practice A
1. proportional
8 4 16 4
; ;
;
10 5 20 5
2. similar
3. congruent
3. 3 
3;33 3
4.
13
3
© Houghton Mifflin Harcourt Publishing Company
Holt McDougal Analytic Geometry