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Warm-Up Exercises
Find the image of the points after the transformation
whose rule is given.
1. (–4, 3), (1, 4), (2, –5),
ANSWER (–6, 4), (–1, 5), (0, –4)
(x, y) → (x – 2, y + 1)
2.
(–2, 1), (3, 5), (–1, –4),
ANSWER
(–1, – 2), (–5, 3), (4, –1)
(x, y) → (–y, x)
3. Find the measure of exterior angle shown.
4. Find x and y.
ANSWER
ANSWER
82, 58
104°
Warm-Up Exercises
Find the image of the points after the transformation
whose rule is given.
4. (2, –4), (–3, 4), (4, –2),
(x, y) → (–x, y)
ANSWER
(–2, –4), (3, 4), (–4, –2)
Constructions
•
•
•
•
Perpendicular line from a point not on the line.
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
Lesson 4.3 Transformations &
Congruence
Transformations change or move a figure to
B'
B
produce a new figure.
Original figure – preimage A
A'
New figure – image
C C'
• A rigid motion is a transformation that preserves
length, angle measure, and area.
• A rigid motion is also called an isometry.
• Translations, reflections, and rotations are
examples of rigid motions.
Warm-Up1Exercises
EXAMPLE
Describe rigid motions to show congruence
Describe the transformation(s) you can use to move the
blue figure onto the red figure.
a.
b.
SOLUTION
a. rotation about P
b. translation and then reflection
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
Describe the transformation(s) you can use to move the
blue figure onto the red figure.
1.
ANSWER
translation and then rotation
2.
ANSWER
translation and then reflection
Warm-Up2Exercises
EXAMPLE
Show figures are not congruent
Explain why figure A and figure B are not congruent
using transformations.
SOLUTION
Translate and then reflect
figure A to compare it to
figure B. Although some of
the corresponding sides are
congruent, the corresponding
angles are not all congruent.
So, the figures are not
congruent.
Warm-Up3Exercises
EXAMPLE
Move one figure in a pattern onto another
QUILTING The quilt shown is
made using a repeating
pattern.
a.
Describe a transformation
that moves figure A onto
figure B.
b. Explain why figures C and D
are congruent by using the
marked angles and sides.
Warm-Up3Exercises
EXAMPLE
Move one figure in a pattern onto another
SOLUTION
a.
A translation or a rotation will move figure A onto
figure B.
b. Figures C and D are congruent because all pairs of
corresponding sides and all pairs of corresponding
angles are congruent.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 2 and 3
Tell whether the two figures in the quilt are congruent
or not congruent. If they are congruent, describe the
transformation(s) you can use to move figure A onto
figure B.
3.
ANSWER
not congruent
4.
ANSWER
congruent; reflection
Daily
Homework
Quiz
Warm-Up
Exercises
1. Identify the transformation(s) you can use to move
figure A onto figure B.
ANSWER
translation, then reflection
Daily
Homework
Quiz
Warm-Up
Exercises
4. Tell whether a rigid motion can move figure A
onto figure B. Explain.
ANSWER
No; a reflection maps one side to a
congruent side, but the other sides are not
congruent.