# Module 3 Unit 1 Notes

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6th Grade Module 3 Unit 1 Day 1 Notes
GEOMETRY Vocabulary:

Point-­‐

an
exact
loca*on,
represented
by
a
______________ Line-­‐
a
straight
path
through
__________
extending
forever
in

opposite
direc*ons

Ray-­‐
part
of
a
line,
has
one
_____________
and
extends
in
the
Line
segment-­‐
part
of
a
line,
with
____________endpoints
other
direc*ons

Plane-­‐
ﬂat
surface
that
has
_________
thickness,
extends
forever                  Congruent-­‐
ﬁgures
with
___________shape
and
size
(EQUAL)

Angle-­‐
two
_______________with
a
common
endpoint                                         Vertex-­‐
the
common
________________________

Right
angle-­‐
_____________angle                                                                Acute
angle-­‐
angle
measuring
greater
than
____________
and

less
than
_____________

Obtuse
angle-­‐
angle
measuring
greater
than
________________                             Straight
angle-­‐
_________________angle

and
less
than
______________________

Complementary
angles-­‐
the
________of
two
angles
is
Supplementary
angles-­‐
the
__________of
two
angles
is

_______________                                                                                   ____________________

Example 1:                                                                                       List:
three points
K
M                                                                       three lines
N
a plane
J                   L
three rays

three line segments

Example 2:                                                                                               Find the measure of each angle and describe the
R                                                           angle type.
a) PQR
S
b) RQS
60o
P                   90o                       30o
30o                                                                                       c) UQR
Q                            T
d) PQT
U

Use the figure to complete the statements.

a) ≮RQS and ≮SQT are ________________________________angles

b) ≮PQS and ≮SQT are ________________________________angles
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Line and Angle Relationships Notes
Geometry
Vocabulary:

Perpendicular
lines-­‐
lines
that
intersect
at
_______________angles                Parallel
lines-­‐
lines
in
the
same
plane
that
do
not

__________________

Skew
lines-­‐
lines
that
do
not
intersect
and
are
not
angles-­‐
two
angles
that
share
a

(they
are
in
diﬀerent
planes!)                                                 ______________and
_________________,
but
no

common
interior
points

VerFcal
angles-­‐
____________________angles
formed
when
two
lines         Transversal-­‐
a
line
that
___________________two
or

intersect.                                                                  more
lines
that
lie
on
the
same
plane

Corresponding
angles-­‐
angles
in
corresponding
____________________   Interior
angles-­‐
angles
__________________
the
two

(In
the
same
posi*on
in
rela*on
to
the
transversal)  parallel
lines
(with
transversal)

Alternate
interior
angles-­‐
interior
angles
on
____________________
sides
Exterior
angles-­‐
angles
___________________the

of
the
transversal                                                           parallel
lines
(with
transversal)

Alternate
exterior
angles-­‐
exterior
angles
on
_____________________
Sides
of
the
transversal

a)  Name all pairs of adjacent, supplementary angles.
1
4                  2
3
b)        Name the vertical angles.

Example 2: Using Vertical Angles
a) Given that m≮1 = 75o, find m≮3.
1
2
4       3                                                b) Find the m≮2.

c) Find the m≮4.

d) Name 2 adjacent, supplementary angles.
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Review Line and Angle Relationships Notes

Example 1: Identifying Parallel, Perpendicular, and Skew Lines
Tell whether the lines in the figure appear parallel, perpendicular, or skew.

a)     AB and AC

b)     CG and BD

c)     AC and BD

Example 2: Using Angle Relationships to Find Angle Measures
Line n ll p. Find the measure of each angle.

≮1                     ≮4

≮2                     ≮5

≮3                     ≮6
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Classifying Polygons Notes
Geometry Vocabulary:

Polygon- a simple, closed plane figure formed by      Regular polygon- polygon with all sides and all
___________ or more line segments                     angles ____________

Examples:                     Non-Examples:

Example 1:
Determine whether each figure is a polygon. It if is not, explain why not.

Example 2:
Name each polygon.

Example 3:
Name each polygon and tell whether it is a regular polygon. If it is not, explain why not.
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Classifying Triangles Notes

Example 1: Classify each triangle by its sides and then by its angle measures.

Example 2:
Identify the different types of triangles in the figure, and determine how many of
each there are.
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Geometry Vocabulary:

_____________and _______________.
(Opposite angles are ≅)

Rectangle- parallelogram with ______________right
angles and ______________________ sides
are congruent.

Rhombus- parallelogram with
_____________congruent sides.

Square- parallelogram with ______________congruent
sides and four _________________angles.

Trapezoid- exactly one pair of opposite sides is
______________

Example 1:
Give all of the names that apply to each quadrilateral. Then give the name that best
describes it.

Example 2:
Draw each figure. If it is not possible to draw, explain why.

a)   A rectangle that is not a square.             b)   A rectangle that is not a parallelogram.
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Interior Angle Sums of Triangles and Quadrilaterals Notes

The sum of the angles in a triangle equal 180˚

Find the unknown angle measure in the triangle.

Example 1:                                         Example 2:

Example 3:
A right triangle with one angle measure of 36o

The sum of the angles in a quadrilateral equal 360˚

Find the unknown angle measure in the quadrilateral.

Example 4:                                        Example 5:

Example 6:
A quadrilateral with angle measures of 144o, 84o, and 48o
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Interior Angles of Polygons Notes

Triangle- interior angles equal _____________________

All polygons- divide it into triangles, multiply ______________________ by the number of
triangles

Example 1:
Divide the polygon into triangles to find the sum of its angle measures.

Example 2:
Find the sum of the interior angles of each polygon.

Example 3:

Number of Number of
Figure
Sides   Triangles

Pentagon              5

Hexagon               6

**The number of triangles is always 2 less than the number of sides of the figure.

Example 4: Find the sum of the interior angles.
November 30, 2012
November 30, 2012

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November 30, 2012
Similar and Congruent Figures Notes
Similar figures- figures with the same ______________________, but not the same size

Congruent figures- similar figures that have the same ____________ AND the same __________­­_

Corresponding angles- angles that are in the same

_______________________ in the shape

Corresponding sides- sides that are in the same

_______________________ in the shape

Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether
the triangles are similar.

Example 1:
Are these figures similar?

a)                                                        b)

Example 2:
Find the unknown measure in the similar figures.

a)                                                 b)

Example 3:
Determine whether the figures are congruent.

Example 4:
Determine the unknown measure in each set of congruent polygons.
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ISTEP Packet

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Transformations and Symmetry Notes
Transformations- changing the ______________________of a geometric figure

Types of Transformations
Translation- __________________             Reflection- ___________________

Rotation- __________________

Example 1:
Name the transformation in each figure.

Example 2:
Decide whether each of the figures has line symmetry. If it does, draw all the lines of
symmetry.

Line Symmetry- drawing a line down the _____________________of a figure, producing the exact
same image on both sides of the line
Rotational Symmetry- figure is rotated less than 360o and it is the original shape

Example 3:
Tell how many times each figure will show rotational symmetry within one full rotation.
November 30, 2012

Welcome to Class!
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November 30, 2012

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GOOD LUCK
November 30, 2012

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