Download Answers for the lesson “Relate Transformations and Congruence”

LESSON
4.3
Answers for the lesson “Relate
Transformations and Congruence”
Skill Practice
Problem Solving
10. No; a reflection maps one side to
26. a. Check students’ rotations.
a congruent side, but other sides
are not congruent.
26. b. Sample answer: Yellow tiles
that share an edge can be
rotated either 728 around the
vertex of the smaller angle
or 1088 around the vertex of
the larger angle. Red tiles that
share an edge can be rotated
368 around the vertex of the
smaller angle or 1448 around
the vertex of the larger angle.
11. yes; reflection in the line y 5 x
12. yes; translation 3 units right and 2
units down
13. yes; rotation 908 counterclock-
wise about the origin
14. yes; translation 3 units right and 5
units up
15. No; a rotation does not map one
26. c. Sample answer: You can
calculate the angles of the
tiles by observing how many
of each type meet at various
vertices in the design.
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figure onto the other, because
corresponding sides lengths are
not congruent.
16. Sample answer: The function rule
describes a translation 3 units
to the right and 1 unit down. A
translation is a rigid motion.
17. Sample answer: The function rule
moves points 1 unit to the left and then
stretches points vertically away from
the x-axis. The transformation is not
a rigid motion, because lengths and
angles are not preserved. The triangle
with vertices (0, 0), (1, 0), and (1, 1)
is transformed to a taller triangle with
vertices (21, 0), (0, 0), and (0, 2).
28. a. The rigid motion of reflection
across a vertical line maps nRTX
onto nV T X, so nR T X ø nV T X.
28. b. The same rigid motion that maps
nRTX onto nVTX also maps nSTW
onto nUTW, so nSTW ø nUTW.
Because the triangles are congruent, the corresponding sides are
congruent, so SW 5 UW.
28. c. SW 5 8 ft; by the Pythagorean
Theorem, TW ø 13.9 ft
.
Geometry
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