Name ________________________________________ Date __________________ Class __________________
LESSON
2-2
Congruence and Transformations
Review for Mastery: Similarity and Congruence Transformations
A transformation is a change in the size or position of a figure.
• A dilation will change the size of a figure unless
the scale factor is 1.
• A translation will slide the figure horizontally
and/or vertically.
• A rotation will turn the figure around the origin.
• A reflection will flip the figure across an axis.
The table below shows how the coordinates change with each type
of transformation.
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Transformation
Coordinate Mapping
Translation
(x, y) o (x a, y b) translates left or right a units
and up or down b units
Reflection
(x, y) o (x, y) reflects across the y-axis
(x, y) o (x, y) reflects across the x-axis
Rotation
(x, y) o (x, y) rotates 180q around origin
(x, y) o (y, x) rotates 90q clockwise around origin
(x, y) o (y, x) rotates 90q counterclockwise around origin
Dilation
(x, y) o (kx, ky) enlarges or shrinks by a scale factor k
Identify the transformation, and tell whether the two figures are similar or congruent.
Original: A(1, 2), B(5, 2), C(3, 7)
Original vertex
Image vertex
Image: A'(0.5, 1), B'(2.5, 1), C'(1.5, 3.5)
A (1, 2)
Ac 0.5(1, 2) (0.5, 1)
Look for a relationship between the
B (5, 2)
Bc 0.5(5, 2) (1.5, 1)
coordinates of the vertices.
C (3, 7)
Cc 0.5(3, 7) (1.5, 3.5)
The image values are half the original.
This is a dilation with scale factor k 0.5. The figures are similar; not congruent.
Identify the transformation from the original to the image, and
tell whether the two figures are similar or congruent.
1. Original: A(2, 4), B(5, 1), C(5, 4)
Image: A'(2, 4), B'(5, 1), C'(5, 4) ________________________________
2. Original: A(8, 2), B(4, 7), C(7, 2)
Image: A'(2, 8), B'(7, 4), C'(2, 7) ________________________________
2-13
Holt McDougal Mathematics
Answers for Lesson 2-2
4. Rotation 180q around origin;
congruent
5. Dilation by scale factor of 4; similar
6. Translation 3 units right and 1 unit
down; congruent
Practice A
1. Translation 3 units right; congruent
2. Reflection across the y-axis;
congruent
3. Dilation by scale factor of 2; similar
7. Rotation 90q clockwise around origin;
congruent
8. Reflection across the line x = 2;
congruent
4. Rotation 180q around origin;
congruent
5. Translation 1 unit right and 1 unit up;
congruent
Review for Mastery
1. Reflection across the y-axis;
congruent
1
; similar
2
7. Reflection across the x-axis;
congruent
6. Dilation by scale factor of
2. Rotation 90q counterclockwise;
congruent
8. Rotation 90q clockwise around origin;
congruent
Challenge
Answers will vary. Monitor that students
have included all 4 types of
transformations and that they are
including enough pages for smooth
transitions between objects.
Practice B
1. Rotation 180° around origin;
congruent
2. Translation 5 units right and 1 unit
down; congruent
3. Dilation by scale factor of 3; similar
4. Reflection across the x-axis;
congruent
5. Rotation 90° clockwise around origin;
congruent
6. Reflection across the y-axis;
congruent
1. Reflection across the y-axis;
congruent
2. Translation of 3 units left and 3 units
up; congruent
3. Dilation with scale factor of 1.5;
similar
4. Rotation of 180°; congruent
5. B
6. J
7. C
8. J
2
; similar
3
8. Rotation 90° counterclockwise around
origin; congruent
Reading Strategies
Practice C
1.
2.
3.
4.
1. Reflection across the y-axis;
congruent
2. Translation 5 units left and 3 units up;
congruent
3. Dilation by scale factor of
1
; similar
5
A14
reflection across the y-axis; congruent
dilation with scale factor 0.5; similar
180° clockwise rotation; congruent
translation 2 units right and 3 units
down; congruent
Holt McDougal Mathematics
© Houghton Mifflin Harcourt Publishing Company
7. Dilation by scale factor of
Problem Solving