Download 2-23 AngleRelationships

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2-23 Angle Relationships Notes
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Name: _______________________________________
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Investigating rotational symmetry.
Rotational Symmetry: ________________________________________________________________
__________________________________________________________________________________
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1. Obtain tracing paper0.0and
rotate around the center of each object. Which objects below have
°
rotational symmetry?
a) On one of the acute angles on your traced parallelogram, shade it and rotate 180°. Because of
_______________________ symmetry, ___________________________ angles in a
parallelogram are ____________________________.
b) Because of rotational symmetry, the angles in the equilateral triangle are all ______________.
c) Because of ___________________________________, the opposite sides in a rectangle are
__________________________.
d) The kite does not have rotational symmetry. The kite does have a ____________________ of
symmetry. Because of that fact, what two angles must be the same. Mark the angles on your
figure.
2. Angle relationships with lines cut by a transversal.
Transversal: _____________________________________________________________________
Parallel:_________________________________________________________________________
Labeling:
Lines
A
A
B
C
B
Angles
C
A
D
C
B
°
a) The transversal in53.2
the
following diagram is: _________________
53.2
°
i. Shade x .
ii. On your tracing paper, trace x . Use this tracing to overlay on other angles to find all
x.
126.8 ° angles congruent to
53.2 °
126.8 °
53.2 °
53.2°°
53.2
53.2 °
26.8 °
°
Segments
53.2 °
D
b) The transversal in the following diagram is: _________________
i. Shade x .
ii. On your tracing paper, trace x . Use this tracing to overlay on other angles to find all
angles congruent to x .
J’
a
L’
b
c d
M’
w
N’
y
K’
x
z
P’
2-23 Assignment
Name: ____________________________
1. State the angle relationship for the following given angles with regards to the diagram.
a)
a and
z ____________
b)
a and
d ____________
a)
a and
c ____________
b)
x and
c ____________
a)
a and
w ____________
b)
w and
d ___________
a)
y and
b ____________
b)
x and
b ____________
a)
x and
d ____________
b)
c and
d ____________
2. Find the values for x and y if you can.
a.
c.
3. For each diagram, find the value of x if possible.
4. Find the measure of each lettered angle.
a)
b)
c)
a = ____________
a = ____________
a = ____________
b = ____________
b = ____________
b = ____________
c = ____________
c = ____________
c = ____________
d)
e)
a = ____________
b = ____________
c = ____________
a = ____________
d = ____________
b = ____________
e = ____________
c = ____________
d = ____________
e = ____________
f = ____________
g = ____________
h = ____________
i = ____________
5. What is wrong with this picture?
6. A tree on a 30° slope grows straight up. What
are the greatest and smallest measures of the
angles the tree makes with the hill? Explain.
6. Circle all letters that have both horizontal and vertical symmetry.
1
2
x  1, y   x  5
3
3
a) What is the point where the two lines intersect?
7. Graph: y 
b) What is a linear equation?
Look up the answer either in your
book or use the internet.
c) What is a system of equations? Look up the answer either in
your book or use the internet.
8. Graph: 3x  2 y  8,
3x  2 y  12
What is the point where the two lines intersect?
9. Graph: 5 x  2 y  8,
10x  4 y  16
What is the point where the two lines intersect?
10. Scientist, Dr. Monika Hardworking, has been illegal experimenting again by irradiating
caterpillars to see if she can make them grow faster and larger. Examine her data below.
Weeks after
2
5
8
10
hatching
Mass (grams)
14g
19g
26g
28g
a) Choose a good scale and
graph the age on the x-axis
and the mass on the y-axis.
b) Using a ruler, draw the
line of best fit making sure
you cross two points you
are certain of the
coordinates.
c) Find the slope using the
two points you crossed in
(b).
d) What does the slope represent in context of this problem?
e) Find the equation of the trend line.
f) What does the y-intercept represent in the context of this problem?
g) Using your trend line, approximately how old this is this 90g irradiated caterpillar?