Transcript Glencoe Geometry - Dolfanescobar's Weblog

Five-Minute Check (over Lesson 4–6)
NGSSS
Then/Now
New Vocabulary
Key Concept: Reflections, Translations, and Rotations
Example 1: Identify Congruence Transformations
Example 2: Real-World Example: Identify a Real-World
Transformation
Example 3: Verify Congruence after a Transformation
Over Lesson 4–6
Name two congruent segments
if 1  2.
A.
0%
B
A
D.
0%
0%
A
B
C
D
0%
D
C.
A.
B.
C.
D.
C
B.
Over Lesson 4–6
A. R  W
0%
B
D. S  T
A
0%
0%
A
B
C
D
0%
D
C. S  U
C
B. S  V
A.
B.
C.
D.
Over Lesson 4–6
Find m R if m RUV = 65.
A. 30
B. 40
0%
B
A
0%
0%
A
B
C
D
0%
D
D. 60
C
C. 50
A.
B.
C.
D.
Over Lesson 4–6
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Find mC if ΔABC is isosceles with AB  AC and
mA = 70.
A. 45
A
0%
B
0%
D. 110
A
B
C
0%
D
D
C. 70
A.
B.
C.
0%
D.
C
B. 55
Over Lesson 4–6
Find x if ΔLMN is equilateral with LM = 2x – 4,
MN = x + 6, and LN = 3x – 14.
A. 20
A
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B
0%
D. 2
A
B
C
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D
D
C. 5
A.
B.
C.
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D.
C
B. 10
Over Lesson 4–6
In the isosceles triangle BCD, C is the vertex
angle. Which sides are congruent?
A. BC  CD
A
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B
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D. no sides are congruent
A
B
C
0%
D
D
C. BD  CD
A.
B.
C.
0%
D.
C
B. BC  BD
MA.912.G.2.4 Apply transformations to polygons to
determine congruence, similarity, and symmetry.
Know that images formed by translations,
reflections, and rotations are congruent to the
original shape. Create and verify tessellations of the
plane using polygons.
MA.912.G.2.6 Use coordinate geometry to prove
properties of congruent, regular and similar
polygons, and to perform transformations in the
plane.
MA.912.G.4.3 Construct triangles congruent to given
triangles.
You proved whether two triangles were
congruent. (Lessons 4–3, 4–4, and 4–5)
• Identify reflections, translations, and
rotations.
• Verify congruence after congruence
transformation.
• transformation
• translation
• congruence
transformation
• rotation
• preimage
• image
• isometry
• reflection
Identify Congruence Transformations
A. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image
are in the same position, just
5 units right and 2 units down.
Answer: This is a translation.
Identify Congruence Transformations
B. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image are
the same distance from the
origin. The angles formed by
each pair of corresponding
points and the origin are
congruent.
Answer: This is a rotation.
Identify Congruence Transformations
C. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image are
the same distance from the
x-axis.
Answer: This is a reflection.
A. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
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D
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C
0%
B
D. none of these
A
0%
A.
B.
C.
D.
A
B
C
D
B. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
0%
D
0%
C
0%
B
D. none of these
A
0%
A.
B.
C.
D.
A
B
C
D
C. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
0%
D
0%
C
0%
B
D. none of these
A
0%
A.
B.
C.
D.
A
B
C
D
Identify a Real-World Transformation
BRIDGES Identify the type of congruence
transformation shown by the image of the bridge
in the river as a reflection, translation, or rotation.
Answer: The image is a
reflection, with the line at which
the bridge meets the water as
the line of reflection.
B. translation
C. rotation
0%
B
D. none of these
A
0%
A.
B.
C.
D.
A
B
C
D
D
A. reflection
C
GAME Identify the type
of congruence
transformation shown by
the image of the chess
piece as a reflection,
translation, or rotation.
0%
0%
Verify Congruence after a Transformation
Triangle PQR with vertices P(4, 2), Q(3, –3), and
R(5, –2) is a transformation of ΔJKL with vertices
J(–2, 0), K(–3, –5), and L(–1, –4). Graph the original
figure and its image. Identify the transformation and
verify that it is a congruence transformation.
Understand
You are asked to identify the type of
transformation—reflection, translation,
or rotation. Then, you need to show
that the two figures are congruent.
Plan
Use the Distance Formula to find the
measure of each side. Then show that
the two triangles are congruent by SSS.
Verify Congruence after a Transformation
Solve
Graph each figure. The transformation
appears to be a translation 6 units right
and 2 units up. Find the measures of the
sides of each triangle.
Verify Congruence after a Transformation
Verify Congruence after a Transformation
Answer: By SSS, ΔJKL  ΔPQR.
Check
Use the definition of a translation.
Use a ruler to measure and compare
each side of the triangles. The sides
are congruent, so the triangles are
congruent.
Triangle ABC with vertices A(–1, –4),
B(–4, –1), and C(–1, –1) is a
transformation of ΔXYZ with vertices
X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph
the original figure and its image.
Identify the transformation and verify
that it is a congruence transformation.
D.
A
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D
C.
A
B
C
D
C
B.
B
A.
A.
B.
C.
D.