Download Station - Parallel Lines and Transversals-

Station
- Parallel Lines and Transversals-
When a transversal intersects a pair of parallel lines, eight angles are formed that have a
unique set of relationships.
Corresponding Angles: Each pair of these angles are the ones at the same location at
each intersection. When the transversal intersects parallel lines corresponding angles are
congruent.
Alternate Interior Angles: Each pair of these angles are inside the parallel lines, and on
opposite sides of the transversal. When the transversal intersects parallel lines Alternate
Interior angles are congruent.
Alternate Exterior Angles: Each pair of these angles are outside the parallel lines, and on
opposite sides of the transversal. When the transversal intersects parallel lines Alternate
Exterior angles are congruent.
If you know the measure of any one angle, you can determine the measure of all other
angles.
Station
- Parallel Lines and Transversals-
1) a and h are ________________________________________
2) g and f are _________________________________________
3) b and g are _________________________________________
4) a and d are _________________________________________
5) c and e are _________________________________________
a
c
b
d
g
h
e
f
6a) If mf = 48°, determine mc.
6b) Explain how you determined your answer. Use words, symbols, or both
in your explanation.
Station
- Parallel Lines and Transversals-
Station
- Constructions-
Constructing a Congruent Line Segment
Draw a ray that is
clearly longer
than the segment
you are trying to
“copy”.
Measure the
distance between
the endpoints of
the line segment
with the compass.
Place the stylus on
the end of your
ray, and draw an
arc with your
compass.
Where the arc
intersects the
ray draw a
point.
Constructing an Angle Bisector
Place the stylus of
your compass on
the vertex of the
angle and draw an
arc that intersects
both rays
Draw points where
the arc intersects
the rays of the
angle.
From each point
drawn in the last
step, draw an arc
above the angle.
Draw a point
where they
intersect
Draw a ray
from the
vertex
through the
last point
drawn.
Station
- Constructions-
Bisect the following angles:
Construct a Congruent Line Segment for each
segment below:
C
A
B
D
Station
- Constructions-
Construct the perpendicular bisector of the line segment below.
Where the bisector intersects the line segment four angles will be formed.
Construct the angle bisector of each one of those angles
Construct at least 4 circles to complete your “design”.
Station
- Missing Angle in a Quadrilateral-
Finding the Third Angle of a Triangle
The sum of the interior angles of a triangle are equal to 180o.
To find the third angle of a triangle when the other two angles
are known, add the two given angles and subtract their total
from 180o.
Example: How many degrees are in the third angle of a
triangle whose other two angles are 40o and 65o? Answer: 180o
- 40o - 65o = 75o
Finding the Fourth Angle of a Quadrilateral
A quadrilateral is a four-sided polygon with four angles. There are
many kinds of quadrilaterals. The five most common types are the
parallelogram, the rectangle, the square, the trapezoid, and the
rhombus.
The sum of the interior angles of a quadrilateral are equal to
360o. To find the missing angle of a quadrilateral when the
other three angles are known, add the three given angles and
subtract their total from 360o.
Example: What is the missing angle in the following
quadrilateral?
360o - 110o - 90o - 90o = 70o
Station
- Missing Angle in a Quadrilateral-
What is the missing angle in the following examples?
34°
?°
What is the fourth angle in a quadrilateral, if the first three
angles total 294 degrees?
Station
- Missing Angle in a Quadrilateral-
Pentagon
hexagon
octagon
 By drawing lines from one vertex to all of the other vertices in a
polygon, the polygon is split into triangles.
 Notice that the pentagon above is split into 3 triangles.
 What is the sum of the angles in a triangle? ____
 Since there are three triangles in the pentagon, what would the sum of
the angles in a pentagon be? ____
Repeat the steps above to determine the number of degrees in a hexagon and
octagon. Complete the chart below
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Septagon
Octagon
Nonagon
Decagon
# of sides
3
4
#of triangles
1
2
Sum of angles
180
360
7
9
10
What patterns do you notice that would help you determine the number of
degrees in a polygon with 15 sides?
Station
- Congruence and Similarity-
Congruent Figures
Study these two triangles. How are they alike? If we rotated the one triangle
and slid it on top of the other one, the two would fit on top of each other
exactly. All the sides and all the angles are equal, so these two triangles are
congruent.
If two figures are congruent, then their corresponding parts are congruent.
Let's look at the corresponding parts of triangles ABC and DFE.
A triangle has three sides and three angles. If two triangles are congruent,
then the sides and angles that match are called corresponding parts. Here,
angle A corresponds to angle D, angle B corresponds to angle F, and angle C
corresponds to angle E. Side AB corresponds to side DF, side BC
corresponds to side FE, and side CA corresponds to side ED.
Similar figures
If two objects have the same shape but not the same size, they are
called "similar." When two figures are similar, the ratios of the lengths
of their corresponding sides are equal. To determine if the triangles
shown are similar, compare their corresponding sides.
Station
- Congruence and Similarity-
These triangles are congruent, name all the corresponding parts (angles and
sides)
There should be six results in all 
Answer all of the following questions on the following drawing …
ABC ~ DEF
1) Are these two triangles similar or congruent? Why??
2) Answer the following statements (be prepared to tell why)
Which angle is congruent with EDF ? ______
Which side corresponds to BA ?______
Which side is corresponds to BC ? ______
Station
4 cm
- Congruence and Similarity-
5 cm
3 cm
8 cm
10 cm
6 cm
Determine the area of the two triangles
Smaller:
Larger:
Write a ratio of the area of the smaller triangle to the larger triangle
A different triangle has a base of 10 in and a height of 4 in.
Determine the area of this triangle.
Double the base and height of the triangle, then determine its area.
Write a ratio of the area of the smaller triangle to the larger
triangle.
What is true about similar triangles when the sides are doubled?
Station
- Transformations (translations and reflections)
A translation means to slide the figure.
When you slide a figure, it is like picking it up
and moving it to somewhere else on the graph. It
doesn’t change it’s orientation.
A reflection is a “flip” or mirror image of the figure.
Sometimes we reflect across the x or y axis,
and sometimes just over another line.
Notice that the
point A and it’s
reflection Aare
both 2 units away
from the line A is
reflected over.
A
A
Station
- Transformations (translations and reflections)
Plot the listed ordered pairs onto the coordinate plane and
connect them together in order to create an enclosed figure.
A(-3,2) B(-7,4) C(-5,8)
Reflect the figure across the dark line
to get the figure ABC  .
Write the ordered pairs of the image below:
A( , )
B( , )
C ( , )
Station
- Transformations (translations and reflections)
Write the ordered pairs for each vertex of the quadrilateral below
(
,
)
(
,
)
(
,
)
(
,
)
Multiply the x and y values of each original ordered pair by two,
and then graph the figure in a different color. What do you notice?
( , )
( , )
( , )
( , )
Divide the x and y values of each original ordered pair by two, and
then graph the figure in a different color. What do you notice?
( , )
( , )
( , )
( , )
Station
- Transformations- Rotation-
A ROTATION is a TURN.
The turn can be made clockwise or counterclockwise
When you rotate around the point of origin, you can
“visualize” where the figure will rotate to
by turning the paper.
90° is a quarter turn of the paper
180° is a half turn of the paper
Turn the paper and write down the new ordered pairs
…then turn the paper back and plot the new points!
Station
- Transformations- Rotation-
Plot the listed ordered pairs onto the coordinate plane and
connect them together in order to create an enclosed figure.
A(3,-2) B(7,-4) C(5,-8)
Rotate the figure 90º clockwise
to get the figure ABC  .
Write the ordered pairs of the image below:
A( , )
B( , )
C ( , )
Station
- Transformations- Rotation-
Draw a figure/design in one of the
quadrants. Rotate the figure 90°
clockwise and draw the new figure.
Rotate 90° clockwise again and draw the
new figure. Rotate 90° clockwise one last
time and draw the new figure.
Station
- Angle Relationships-
Angle Relationship
Definition
Adjacent
A pair of nonoverlapping angles
that share a
common side and
vertex.
A pair of angles
that have a sum of
90°.
Complementary
Examples
a
ab
b
a
b
Supplementary
A pair of angles
that have a sum of
180°.
Vertical
A pair of angles
across from one
another formed
when two lines
intersect.
b
a\
b
a
a b
b
\
\
b
When two angles are supplementary, they have a sum
b
of 180°. So if you know the measure of one, you can
subtract it from 180 to find the measure of the other!
When two angles are complementary, they have a
sum of 90°. So if you know the measure of one, you
can subtract it from 90 to find the measure of the
other!
When two angles are vertical, they are also
congruent. So if you know the measure of one, the
other is the same number of degrees!
Station
- Angle Relationships-
e a
d
b
c
1)  a and  b ___________________________
2)  c and  d ___________________________
3)  c and  e ___________________________
4)  a and  e ___________________________
5) Find the measure of every angle if md = 132.
m a = _____ m b = _____ m c = _____ m e = _____
Station
- Angle Relationships-