1) The document discusses determining the coordinates of vertices after a dilation and provides examples. It also discusses congruence and using transformations like rotations, reflections, and translations to determine if two figures are congruent. 2) To determine congruence, you can use transformations to map one figure onto another. If a single or series of transformations can map all points of one figure directly onto the other, they are congruent. 3) Reflections, rotations, and translations will produce congruent figures as they preserve size and shape but change position.

1. Course 3, Lesson 7-1
Determine the coordinates of the vertices of each figure after a
dilation with the given scale factor k.
1. G(0, 0), H(−2, −1), J(5, 3); k = 2
2.
3. Tamar wants to reduce a piece of art that is 8 inches by 10
inches for the club newsletter. The width of the new art must
be 3 inches. What is the length of the new piece of art?
1
3
k

2. Course 3, Lesson 7-1
ANSWERS
1. G’(0, 0), H’(−4, −2), J’(10, 6)
2. A’(1, 1), B’(0, 1), C’(−1, 0), D’(0, −1)
3.
3
3 in.
4

3. HOW can you determine
congruence and similarity?
Geometry
Course 3, Lesson 7-1

4. Course 3, Lesson 7-1 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
• 8.G.1
Verify experimentally the properties of rotations, reflections, and
translations:
• 8.G.1a
Lines are taken to lines, and line segments to line segments of the same
length.
• 8.G.1b
Angles are taken to angles of the same measure.
• 8.G.2
Understand that a two-dimensional figure is congruent to another if the
second can be obtained from the first by a sequence of rotations,
reflections, and translations.
Geometry

5. Course 3, Lesson 7-1 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Geometry

6. To
• identify congruence by using transformation,
• determine the transformations used to map
two congruent figures
Course 3, Lesson 7-1
Geometry

7. Reflect ABC over a vertical line. Label the
vertices of the image A', B', and C'.
1
Need Another Example?
2
3
Step-by-Step Example
1. Determine if the two figures are congruent by using
transformations. Explain your reasoning.
Translate A'B'C' until all sides and angles
match XYZ.
So, the two triangles are congruent because a
reflection followed by a translation will map ABC
onto ZYX.

8. Answer
Need Another Example?
Determine if the two figures are congruent by
using transformations. Explain your reasoning.
congruent; A rotation followed by a
translation maps figure A onto figure B.

9. 1
Need Another Example?
2
Step-by-Step Example
2. Determine if the two figures are congruent by using
transformations. Explain your reasoning.
Reflect the red figure over a vertical line.
Even if the reflected figure is translated up and
over, it will not match the green figure exactly.
The two figures are not congruent.

10. Answer
Need Another Example?
Determine if the two figures are congruent by
using transformations. Explain your reasoning.
Not congruent; no transformations will
match the figures up exactly.

11. 1
Need Another Example?
2
3
Step-by-Step Example
3. Ms. Martinez created the logo shown. What transformations did she
use if the letter “d” is the preimage and the letter “p” is the image?
Are the two figures congruent?
Start with the preimage. Rotate the letter “d”
180° about point A.
Translate the new image up.
A
A
Ms. Martinez used a rotation and translation to
create the logo. The letters are congruent
because images produced by a rotation and
translation have the same shape and size.

12. Answer
Need Another Example?
The pattern below appears along the edge of a
plate. What transformations could be used if the
first figure is the preimage and the second is the
image?
Sample answer: a rotation followed by a
translation

13. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-1
Geometry

14. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-1
Geometry
Sample answers:
• Two figures are congruent if they are the same size and
shape.
• Two figures are congruent if one can be obtained from
the other by a series of rotations, reflections, or
translations.

15. Triangle PQR has vertices
P(3, 4), Q(1, 2), and R(0, –1).
Choose two transformations
to perform on the triangle
and write the new coordinates
of the image. Is your image
congruent to the original figure?
Course 3, Lesson 7-1
Ratios and Proportional RelationshipsFunctionsGeometry