M3: Chapter 13 Notes
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Academic
Chapter 13 Notes
Angle Relationships
and
Transformations
Name____________________Pd.____
M3: Chapter 13 Notes
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Sections 13.1-13.3
Vocabulary Words
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Complementary angles
Supplementary angles
Vertical angles
Transversal
Exterior angle
Interior angle
Alternate exterior angle
Alternate interior angle
Corresponding angles
Sections 13.4-13.7
Vocabulary Quiz
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Transformation
Image
Translation
Tessellation
Reflection
Line of reflection
Line symmetry
Line of symmetry
Rotation
Center of rotation
Angle of rotation
Rotational symmetry
Dilation
Center of dilation
Scale factor
M3: Chapter 13 Notes
Section 13.1: Angle Relationships
Learning Goal: We will classify special pairs of angles.
Vocabulary:
 Complementary angles –
 Supplementary angles –
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M3: Chapter 13 Notes
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Example 1: Identifying Complementary, Supplementary Angles
ON YOUR OWN:
Example 2: Finding an Angle Measure
ON YOUR OWN:
3 and 4 are supplementary. If m3  127 , find m4 .
M3: Chapter 13 Notes
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 Vertical angles – a pair of opposite angles formed when two lines
intersect at one point
Example 3: Using Supplementary and Vertical Angles
ON YOUR OWN:
M3: Chapter 13 Notes
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Section 13.2: Angles and Parallel Lines
Learning Goal: We will identify angles when a transversal intersects lines.
Vocabulary:
 Transversal – a line that intersects two
or more lines at different points
 Corresponding angles – two angles that
occupy corresponding positions when a
transversal intersects two lines
 Alternate interior angles – when a
transversal intersects two lines, two
angles that lie between the two lines on
opposite sides of the transversal
 Alternate exterior angles – when a transversal intersects two
lines, two angles that lie outside the two lines on opposite sides of
the transversal
Example 1: Identifying Angles
In the diagram of the John Hancock Center
in Chicago, line t is a transversal. Tell
whether the angles are corresponding,
alternate interior, or alternate exterior
angles.
a. 1 and 8
b. 2 and 6
a. 4 and 5
M3: Chapter 13 Notes
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ON YOUR OWN:
**When a transversal intersects two parallel lines, the corresponding
angles are equal, the alternate interior angles are equal, and the
alternate exterior angles are equal.
Example 2: Finding Angle Measures
ON YOUR OWN:
**If a transversal intersects two lines so that the corresponding
angles have the same measure, then the lines are ________________.
M3: Chapter 13 Notes
Example 3: Finding the Value of a Variable
ON YOUR OWN:
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M3: Chapter 13 Notes
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Section 13.3: Angles and Polygons
Learning Goal: We will find measures of interior and exterior angles.
Vocabulary:
 Interior angles – an angle inside the
polygon
 Exterior angles – an angle adjacent to
an interior angle of the polygon formed
by extending one side of the polygon
Example 1: Finding the Sum of a Polygon’s Interior Angles
Find the sum of the measures of the interior angles of the polygon.
a.
b.
Example 2: Finding the Measures of an Interior Angle
Find the measure of an interior angle of a regular 11-gon.
M3: Chapter 13 Notes
ON YOUR OWN:
a. Find the sum of the
measures of the interior
angles of a convex decagon.
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b. Find the measures of an
interior angle of a regular
12-gon.
Example 3: Finding an Interior Angle of an Irregular Polygon
A hexagon has interior angles with the measures of 89˚, 111˚, 72˚,
80˚, and 100˚. What is the measure of the sixth angle?
Example 4: Finding the Measure of an Exterior Angle
ON YOUR OWN:
M3: Chapter 13 Notes
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Example 5: An Exterior Angle Measure of a Regular Polygon
Find the measure of an exterior angle of a regular 12-gon.
**The sum of the measures of the exterior angles is _____________.
Example 6: Using the Sum of Measures of Exterior Angles
ON YOUR OWN:
M3: Chapter 13 Notes
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Section 13.4: Translations
Learning Goal: We will translate figures in a coordinate plane.
Vocabulary:
 Transformation – a change made to the location or to the size of
a figure, resulting in a new figure, called the image
 Image – the new figure formed by a transformation
 Translation – a transformation in which each point of a figure
moves the same distance in the same direction
Example 1: Describing a Translation
M3: Chapter 13 Notes
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**You can describe a translation of each point (x, y) of a figure using
____________________ ___________________________.
Example 2: Translating a Figure
Draw quadrilateral DEFG with vertices
D(3, -2), E(3, -3), F(0, -3), and G(1, -2).
Then find the coordinates of the
vertices of the image after the
translation ( x, y)  ( x  4, y  1) , and draw
the image.
ON YOUR OWN:
Draw quadrilateral ΔABC with vertices
A(-1, 0), B(-1, 3), and C(-4, 2). Then find
the coordinates of the vertices of the
image after the translation
( x, y )  ( x  7, y  3) , and draw the image.
M3: Chapter 13 Notes
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 Tessellation – a covering of a plane with a repeating pattern of
one or more shapes, with no gaps or overlaps
Example 3: Creating Tessellations
ON YOUR OWN:
Tell whether you can create a tessellation using only translations of the
given polygon. If you can, create a tessellation. If not, explain why
not.
a.
b.
c.
M3: Chapter 13 Notes
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Section 13.5: Reflections and Symmetry
Learning Goal: We will reflect figures and identify lines of symmetry.
Vocabulary:
 Reflection – a transformation in which a figure is reflected, or
flipped, in a line
 Line of reflection – the line in which a figure is flipped when the
figure undergoes a reflection
Example 1: Identifying Reflection
ON YOUR OWN:
M3: Chapter 13 Notes
COORDINATE NOTATION:
Example 2: Reflecting a Triangle
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M3: Chapter 13 Notes
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ON YOUR OWN:
 Line symmetry – a figure has line symmetry if a line divides the
figure into two parts that are reflections of each other in the
line
 Line of symmetry – a line that divides a figure into two parts that
are reflections of each other in the line
Example 3: Identifying Lines of Symmetry
Tell how many lines of symmetry the flag has.
M3: Chapter 13 Notes
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ON YOUR OWN:
Tell how many lines of symmetry the figure has.
a.
b.
c.
Section 13.6: Rotations and Symmetry
Learning Goal: We will rotate figures and identify rotational symmetry.
Vocabulary:
 Rotation – a transformation in
which a figure is turned through
a given angle, called the angle of
rotation, and in a given direction
about a fixed point
 Center of rotation – the point
about which a figure is turned
when the figure undergoes a
rotation
 Angle of rotation – the angle
formed by two rays drawn
from the center of rotation
through corresponding points
on the original figure and its
image
M3: Chapter 13 Notes
Example 1: Identifying Rotations
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M3: Chapter 13 Notes
Example 2: Rotating a Triangle
180° Rotations:
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M3: Chapter 13 Notes
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Example 3: Rotating a Triangle
 Rotational symmetry – a figure has rotational symmetry if a
rotation of 180˚ or less clockwise (or counterclockwise) about its
center produces an image that fits exactly on the original figure
Example 4: Identifying Rotational Symmetry
Tell whether the figure has rotational symmetry. If so, give each angle
and direction of rotation that produce rotational symmetry.
a.
b.
c.
M3: Chapter 13 Notes
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Section 13.7: Dilations
Learning Goal: We will dilate figures in a coordinate plane.
Vocabulary:
 Dilation – a transformation in
which a figure stretches or
shrinks with respect to a
fixed point
 Center of dilation – the point
with respect to which a figure
stretches or shrinks when the
figure undergoes a dilation
 Scale factor – for a dilation,
the ratio of a side length of
the image to the corresponding side length of the original figure
Example 1: Dilating a Quadrilateral
Draw quadrilateral ABCD with
vertices A(-1, 2), B(3, 1), C(2, -1), and
D(-1, -1). Then find the coordinates
of the vertices of the image after a
dilation having a scale factor of 3,
and draw the image.
M3: Chapter 13 Notes
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Example 2: Using a Scale Factor Less than 1
Draw PQR with vertices P(4, 4) ,
Q(6, 0) , and R(6,  2) . Then find the
coordinates of the image after a
dilation having a scale factor of 0.5
and draw the image.
Example 3: Finding a Scale Factor
A digital photo with dimensions 640 by 460 pixels is reduced to 160 by
115 pixels. Find the scale factor.
ON YOUR OWN:
M3: Chapter 13 Notes
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