Download G7-3 Measuring and Drawing Angles and Triangles

G7-3 Measuring and Drawing Angles and Triangles
right angle
90°
acute angles
obtuse angles less than 90°
more than 90° and less than 180°
1. Without using a protractor, identify each angle as acute or obtuse.
a)
b)
c)
d)
2. Practise choosing the correct scale to measure an angle.
a)
Step 2: Circle the 2 numbers that
the arm of the angle passes through.
Step 3: Choose the correct angle
measure. Example: if the angle is
acute, the measure is less than 90°.
b)
The angle is acute / obtuse.
The angle is acute / obtuse.
The angle measures
The angle measures
c)
°.
d)
The angle is acute / obtuse.
The angle is acute / obtuse.
The angle measures
The angle measures
102
°.
°.
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Step 1: Is the angle acute or obtuse?
Circle your answer.
°.
Geometry 7-3
3. Measure each angle. Hint: For parts d) and e), you will have to extend the arms.
a)
b)
c)
°
°
°
d)
e)
°
°
4. In each polygon, circle angle ÐXYZ . Then measure the angle.
a)
X
b)
Y
Y
X
W
Measure of ÐXYZ :
Z
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COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED
5. ÐABC is 90°. ÐABD is 50°.
U
c)
Z
Z
W
V
Measure of ÐXYZ :
A
V
W
Y
X
Measure of ÐXYZ :
D
50˚
B
a) What is the measure of ÐDBC ?
C
How do you know?
b) Measure ÐDBC with a protractor to check your answer in a).
Geometry 7-3
103
G7-4 Perpendicular Lines
Perpendicular lines meet at a right angle (90°). The ^ symbol means “is perpendicular to.”
EG ^ ZF AB ^ ST
S
Z
E
A
G
F
B
T
1. Name the perpendicular lines.
a)
b) K
c)
S
P
D
A
C
AB
B
E
D
J
E
^
C
F
B
d)
T
^
A
Q
^
^
2. Are the pairs of lines below perpendicular? Measure the angle where they meet to check.
Draw a square corner (
a)
) to show any perpendicular lines.
b)
c)
d)
e)
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COPYRIGHT © 2009 JUMP MATH: NOT TO BE COPIED
3. Match the diagrams to the descriptions.
A.
B.
A
P
B
A
C.
P
B
A
D.
P
B
A
B
P
point P on line segment AB
lines that pass through point P on AB
lines perpendicular to AB
the line perpendicular to AB that passes through point P
Geometry 7-4
105
^
^
^
^
G7-6 Parallel Lines
Parallel lines never intersect, no matter how far they are extended in either direction.
1. Extend both lines. Use a ruler. Do the lines intersect or are they parallel?
2. Match the descriptions to the lines.
A. The lines intersect.
B. If the lines were extended far enough, they would intersect.
C. The lines are parallel.
3. Give two examples of parallel lines in the world around you.
We mark parallel lines using an equal number of arrow symbols (>, >>, and so on). The || symbol
means “is parallel to.”
B
C
Example: AB || CD.
A
D
4. Use arrow symbols to mark the sides or edges of these shapes that look like they are parallel.
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a)
b)
c)
5. State which lines are parallel.
a) A
X
B
Y
AB
Geometry 7-6
F
b)
||
d)
R
T
U
G
S
||
E
c)
H
L
F
G
M
||
109
Determining If Two Lines Are Parallel
If two lines are perpendicular to another line, then they are parallel.
If two lines are parallel, any line perpendicular to one of the
parallel lines will be perpendicular to the other.
6. Mark any parallel lines. State which lines are parallel.
N
U
O
a)
b)
E
B
F
c)
A
D
M
d)
L
R
K
W
X
S
H
V
EF
V
Y
||
B
||
a) AB is parallel to
K
and
KL is perpendicular to CD, so
KL is also perpendicular to
b) AB ||
and QR ^
Q
C
.
, so,QR ^
B
.
R
D
L
A
B
D
C
Mark the right angles on this rectangle.
b) AD ^ AB and AD ^
||
A
8. a) All the angles in a rectangle are right angles.
J
||
7. Complete the statements.
C
DC ^ AD and DC ^
, so AB ||
, so AD ||
c) Explain how you know that these pairs of sides are parallel.
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9. Circle the flags that contain parallel lines (not counting the edges of the flags).
110
Geometry 7-6
G7-7 Angle Relationships
shared arm
a
b
shared vertex
straight angle
A straight angle measures 180°.
a
adjacent angles
Adjacent angles Ð a and Ð b
have a shared vertex and arm.
b
linear pair
The sum of the angles
in a linear pair is 180°.
1. Match the diagrams to the names. Hint: The angles in a linear pair are also adjacent angles.
straight angle:
A.
a
adjacent angles:
B.
b
linear pair:
C.
b
a
a
b
2. Calculate these angle sums.
a) 10° + 25° =
b) 30° + 40° =
c) 12° + 28° =
d) 20° + 30° + 40° =
3. Ð1 and Ð2 are a linear pair. Identify the three other linear pairs in the diagram.
Ð
and Ð
and Ð
Ð
and Ð
Ð
4
1
2
3
4. Determine the sum of the angles formed by two lines that intersect at a right angle.
∠1 + ∠2 = 90 + 90 =
So, ∠1 + ∠2 + ∠3 + ∠4
∠3 + ∠4 = 90 + 90 =
°
°+
°=
°
°
1
2
3
4
5. Determine the sum of the angles formed by any two intersecting lines.
The sum of the angles in a linear pair is
So, ∠1 + ∠2 =
So, ∠1 + ∠2 + ∠3 + ∠4 =
° and ∠3 + ∠4 =
°.
°
30°
112
2
°
Calculate these angle sums to check your prediction.
95°
150°
1
3
°
6. Predict the sum of the four angles around any point P.
4
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150°
30°
30° + 150° + 30° + 150° =
85°
85°
95°
95° + 85° + 95° + 85° =
Geometry 7-7
∠XZY =
∠XZY =
∠A + ∠B + ∠C = 180
∠A
∠A = 180 − (80 + 30 )
∠F
∠A = 180 −
∠A =