Download Answers to Parent Pages L98-L103

Geometry
→ Draw and identify lines and angles, and classify shapes by properties
of their lines and angles.
98
99
100
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102
103
CC.4.G.1
CC.4.G.1
CC.4.G.2
CC.4.G.2
CC.4.G.3
CC.4.G.3
Lines, Rays, and Angles . . . . . . .
Parallel Lines and Perpendicular Lines
Classify Triangles . . . . . . . . . . .
Classify Quadrilaterals . . . . . . . .
Line Symmetry . . . . . . . . . . . .
Find and Draw Lines of Symmetry . .
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Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
vii
Name
1
Lines, Rays, and Angles
LESSON
98
Name
What it looks like
Think
D
point D
A point names a location in space.
‹_›
line AB; AB
‹_›
line BA; BA
A line extends without end in
opposite directions.
B
A
___
line segment AB; AB
___
line segment BA; BA
“Segment” means part. A line
segment is part of a line. It is
named by its two endpoints.
B
A
____›
ray MN; MN
M
____›
ray NM; NM
A ray has one endpoint and extends
without end in one direction. A
ray is named using two points. The
endpoint is always named first.
N
M
N
X
angle XYZ; ∠XYZ
Two rays or line segments that
share an endpoint form an angle.
The shared point is the vertex of
the angle.
angle ZYX; ∠ZYX
Y
angle Y; ∠Y
A right angle
forms a square
corner.
© Houghton Mifflin Harcourt Publishing Company
CC.4.G.1
OBJECTIVE Identify and draw points, lines, line segments, rays, and angles.
Z
An acute angle
opens less than
a right angle.
An obtuse angle
opens more than
a right angle
and less than a
straight angle.
A straight angle
forms a line.
Draw and label an example of the figure. Possible drawings are shown.
___›
___
1. PQ
2. K J
3. obtuse ∠FGH
H
P
Geometry
Q
K
J
F
G
195
Name
1
Lines, Rays, and Angles
CC.4.G.1
Draw and label an example of the figure.
1. obtuse ∠ABC Possible drawings are shown.
A
Think: An obtuse angle is greater than
a right angle. The middle letter, B,
names the vertex of the angle.
C
B
2.
____›
GH
___
3. acute ∠JKL
4. BC
J
>
B
?
C
K
L
Use the figure for 5–8. Possible answers are given.
5. Name a line segment.
6. Name a right angle.
___
∠EJF
EF
C
7. Name an obtuse angle.
D
E
F
G
H
8. Name a ray.
___›
∠CEJ
JD
B
J
© Houghton Mifflin Harcourt Publishing Company
A
Problem Solving
Use the figure at the right for 9–11.
9. Classify ∠AFD.
:
obtuse
9
10. Classify ∠CFE.
right
11. Name two acute angles.
;
8
=
<
Possible answers: ∠AFB and ∠DFE
196
Lesson 98
Name
LESSON
99
1
Parallel Lines and Perpendicular Lines
CC.4.G.1
OBJECTIVE Identify and draw parallel lines and perpendicular lines.
Parallel lines are lines in a plane that are always the same
distance apart. Parallel lines or line segments never meet.
In the figure, lines AB and CD, even if extended, will never meet.
The lines are parallel. Write AB||CD.
Lines AD and BC are also parallel. So, AD||BC.
8
9
;
:
Intersecting lines cross at exactly one point. Intersecting lines that
form right angles are perpendicular.
In the figure, lines AD and AB are perpendicular because
they form right angles at vertex A. Write AD⊥AB.
Lines
BC
and
CD
are also perpendicular. So, BC⊥CD.
Use the figure for 1–3.
M
I
© Houghton Mifflin Harcourt Publishing Company
1. Name two sides that appear to be parallel.
___
___
RV and ST
K
J
2. Name two sides that appear to be perpendicular.
___
___
___
___
RV and RS or RS and ST
3. Name two sides that appear to be intersecting,
but not perpendicular.
___
___
___
___
RV and VT or TV and ST
Geometry
197
Name
1
Parallel Lines and Perpendicular Lines
CC.4.G.1
Use the figure for 1–3.
1. Name a pair of lines that appear to be perpendicular.
8
:
Think: ‹Perpendicular
lines form right angles.
___›
‹__›
AB and EF appear to form right angles.
‹___›
<
‹___›
AB and EF
=
9
;
2. Name a pair of lines that appear to be parallel.
‹___›
‹___›
AB and CD
3. Name another pair of lines that appear to be perpendicular.
‹___›
‹___›
EF and CD
Draw and label the figure described. Possible drawings are shown.
M
‹____›
‹___›
‹___›
5. WX || YZ
N
O
Q
R
P
N
‹__›
6. FH ⊥ JK
=
A
P
B
Q
?
© Houghton Mifflin Harcourt Publishing Company
‹___›
‹____›
4. MN and PQ intersecting
at point R
Problem Solving
Use the street map for 7–8.
7. Name two streets that intersect but do
not appear to be perpendicular.
Maple
Oak and Maple or Oak and Birch
Birch
Oa
k
Elm
8. Name two streets that appear to be
parallel to each other.
Maple and Birch
198
Lesson 99
Name
1
Classify Triangles
LESSON
100
CC.4.G.2
OBJECTIVE Classify triangles by the size of their angles.
A triangle is a polygon with 3 sides
and 3 angles.
Each pair of sides joins at a vertex.
Q
You can name a triangle by its vertices.
ΔPQR
ΔPRQ
ΔQRP
ΔQPR
There are
3
have at least
ΔRPQ
ΔRQP
P
R
types of triangles. All triangles
2
acute angles.
Obtuse triangle
one obtuse angle
Right triangle
one right angle
XZlk\
Acute triangle
three acute angles
XZlk\
acute
XZlk\
acute
XZlk\
fYklj\
acute
i`^_k
© Houghton Mifflin Harcourt Publishing Company
1. Name the triangle. Tell whether
each angle is acute, right, or obtuse.
A name for the triangle
is
ΔXYZ
Z
.
∠X is
acute
.
∠Y is
obtuse
.
∠Z is
acute
.
X
Y
Classify each triangle. Write acute, right, or obtuse.
2.
3.
right
Geometry
4.
acute
obtuse
199
Name
1
Classify Triangles
CC.4.G.2
Classify each triangle. Write acute, right, or obtuse.
1. A
Think: Angles A and C are both acute.
Angle B is obtuse.
B
C
obtuse
D
3.
right
acute
A
200
obtuse
Check students’ drawings.
5. Use figure ABCD below. Draw a
line segment from point B to
point D. Name and classify the
triangles formed.
D
N
M
H
E
Problem Solving
4. L
J
G
6. Use figure ABCD below. Draw a
line segment from point A to point
C. Name and classify the triangles
formed.
B
C
A
D
B
C
Possible answer: triangles ABD and
Possible answer: triangles ADC and
BCD are both obtuse triangles.
ABC are both acute triangles.
Lesson 100
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F
2.
Name
LESSON
101
1
Classify Quadrilaterals
CC.4.G.2
OBJECTIVE Sort and classify quadrilaterals.
4 sides and
A quadrilateral is a polygon with
Some quadrilaterals have special names:
4
angles.
HlX[i`cXk\iXc
+j`[\j
+Xe^c\j
GXiXcc\cf^iXd
)gX`ijf]
gXiXcc\cj`[\j
I\ZkXe^c\
+i`^_kXe^c\j
)gX`ijf]
gXiXcc\cj`[\j
KiXg\qf`[
<oXZkcp(gX`if]
gXiXcc\cj`[\j
I_fdYlj
+j`[\jf]
\hlXcc\e^k_
© Houghton Mifflin Harcourt Publishing Company
JhlXi\
+i`^_kXe^c\j
+j`[\jf]
\hlXcc\e^k_
Classify each figure as many ways as possible. Write
quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.
1.
2.
3.
quadrilateral,
quadrilateral,
quadrilateral,
trapezoid
parallelogram, rectangle,
parallelogram
rhombus, square
Geometry
201
Name
1
Classify Quadrilaterals
CC.4.G.2
Classify each figure as many ways as possible.
Write quadrilateral, trapezoid, parallelogram, rhombus,
rectangle, or square.
1.
Think: 2 pairs of parallel sides
4 sides of equal length
0 right angles
quadrilateral, parallelogram,
rhombus
2.
3.
4.
quadrilateral,
quadrilateral,
parallelogram,
trapezoid
quadrilateral
rectangle
6.
7.
quadrilateral,
quadrilateral,
quadrilateral,
parallelogram,
trapezoid
parallelogram
rhombus
Problem Solving
8. Alan drew a polygon with four
sides and four angles. All four sides
are equal. None of the angles
are right angles. What figure did
Alan draw?
a rhombus
202
9. Teresa drew a quadrilateral with
2 pairs of parallel sides and
4 right angles. What quadrilateral
could she have drawn?
a square or rectangle
Lesson 101
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5.
Name
LESSON
102
1
Line Symmetry
CC.4.G.3
OBJECTIVE Determine whether a figure has a line of symmetry.
Tell whether the parts on each side of the line match.
Is the line a line of symmetry?
Step 1 Trace and cut out
the shape.
Fold the shape along
the dashed line.
Step 2 Tell whether
the parts on each side
match.
Compare the parts on
each side.
no
match
no
match
Step 3 Decide if the line
is a line of symmetry.
The parts on each
side of the line do not
match.
is not
So, the line
a line of symmetry.
The parts do not match.
© Houghton Mifflin Harcourt Publishing Company
Tell if the line appears to be a line of symmetry. Write yes or no.
1.
2.
yes
no
3.
4.
yes
Geometry
no
203
Name
1
Line Symmetry
CC.4.G.3
Tell if the dashed line appears to be a line of symmetry.
Write yes or no.
1.
2.
no
yes
5.
3.
6.
no
4.
yes
7.
yes
no
8.
no
yes
Check students’ drawings.
Complete the design by reflecting over the line of symmetry.
10.
© Houghton Mifflin Harcourt Publishing Company
9.
Problem Solving
11. Kara uses the pattern at the right
to make paper dolls. The dashed
line represents a line of symmetry.
A complete doll includes the
reflection of the pattern over the
line of symmetry. Complete the
design to show what one of Kara’s
paper dolls looks like. Check students’ drawing.
204
Lesson 102
Name
LESSON
103
1
Find and Draw Lines of Symmetry
CC.4.G.3
OBJECTIVE Identify and draw lines of symmetry in two-dimensional figures.
Tell whether the shape appears to have zero lines, 1 line, or
more than 1 line of symmetry. Write zero, 1, or more than 1.
Step 1 Decide if the
shape has a line of
symmetry.
Step 2 Decide if the
shape has another line
of symmetry.
Trace and cut out the
shape. Fold the shape
along a vertical line.
Open the shape
and fold it along a
horizontal line.
Do the two parts match
Do the two parts match
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exactly?
yes
exactly?
So, the shape appears to have
yes
more than 1
Step 3 Find any other
lines of symmetry.
Think: Can I fold the shape in
other ways so that the
two parts match exactly?
I can fold the paper
diagonally two different
ways, and the parts
match exactly.
line of symmetry.
Tell whether the shape appears to have zero lines, 1 line, or
more than 1 line of symmetry. Write zero, 1, or more than 1.
1.
2.
more than 1
Geometry
3.
1
zero
205
Name
1
Find and Draw Lines of Symmetry
CC.4.G.3
Tell whether the shape appears to have zero lines, 1 line,
or more than 1 line of symmetry. Write zero, 1, or more than 1.
1.
2.
1
3.
more than 1
4.
zero
more than 1
Does the design have line symmetry? Write yes or no.
If your answer is yes, draw all lines of symmetry. Check students’ lines of symmetry.
5.
6.
yes
7.
yes
8.
no
yes
Problem Solving
Use the chart for 12–13.
12. Which number or numbers appear
to have only 1 line of symmetry?
3
13. Which number or numbers appear
to have 2 lines of symmetry?
0 and 8
206
Lesson 103
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Draw a shape for the statement. Draw the line or lines of symmetry.
Check students’ drawings.
9. zero lines of symmetry
10. 1 line of symmetry
11. 2 lines of symmetry