Transcript Lesson

Lesson 4-7
Congruence Transformations
5-Minute Check on Lesson 4-6
Transparency 4-7
Refer to the figure.
1. Name two congruent segments if 1  2.
2. Name two congruent angles if RS  RT.
3. Find mR if mRUV = 65.
4. Find mC if ABC is isosceles with AB  AC and mA = 70.
5. Find x if LMN is equilateral with LM = 2x – 4, MN = x + 6,
and LN = 3x – 14.
6.
Find the measures of the base angles of an
isosceles triangle if the measure of the vertex angle is 58.
Standardized Test Practice:
A
32
B
58
C
61
D
122
5-Minute Check on Lesson 4-6
Transparency 4-7
Refer to the figure.
1. Name two congruent segments if 1  2.
UW  VW
2. Name two congruent angles if RS  RT.
S  T
3. Find mR if mRUV = 65. 50
4. Find mC if ABC is isosceles with AB  AC and mA = 70. 55
5. Find x if LMN is equilateral with LM = 2x – 4, MN = x + 6,
and LN = 3x – 14.
10
6.
Find the measures of the base angles of an
isosceles triangle if the measure of the vertex angle is 58.
Standardized Test Practice:
A
32
B
58
C
61
D
122
Objectives
• Identify reflections, translations, and
rotations
• Verify congruence after a congruence
transformation
Vocabulary
• Transformation – operations that map a figure into
another figure
• Preimage – a figure before it is moved
• Image – a figure after it has been moved
• Congruence transformation – a rigid transformation
that main the figures size and shape
• Isometry – a rigid transformation
• Reflection – a flip, reflects the figure over a line of
reflection
• Translation – a slide, moves the figure up or down; left
or right; or a combination of the two
• Rotation – a turn, is a transformation about a fixed
point called the center of rotation
Key Concept
Identify Congruence Transformations
• 1A. 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
• 1B. 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
• 1C. 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.
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.
Verify Congruence after 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.
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 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.
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 Transformation
• Verify that it is a congruence transformation.
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 Transformation
• Verify that it is a congruence transformation.
Answer: By SSS, ΔJKL  ΔPQR.
Summary & Homework
• Summary:
– In a congruence transformation, the position of
the image may differ from the preimage, but the
two figures remain congruent.
– Flips, turns, and slides are congruence
transformations
• Homework:
– pg 297-8: 7-12, 13-16