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WEEK 13 (assignments 42-45)
Videos: Constructing Parallel Lines:
http://www1.teachertube.com/viewVideo.php?video_id=203474&title=Parallel_Lines_Construction
http://teachertube.com/viewVideo.php?video_id=120198&title=Constructing_Parallel_Lines
Given a line and a point, construct a line through the point, parallel to the given line using Corresponding Angles
(CA)
1. Begin with point P and
2. Draw an arbitrary line
3. Center the compass at
4. Set the compass radius to
line k.
through point P, intersecting
point Q and draw* an arc
the distance between the two
line k. Call the intersection
intersecting both lines.
intersection points of the first
point Q. Now the task is to
Without changing the radius
arc. Now center the compass
construct an angle with
of the compass, center it at
at the point where the second
vertex P, congruent to the
point P and draw another
arc intersects line PQ. Mark
angle of intersection.
arc.
the arc intersection point R.
5. Label the new line PR
6. Box a statement to show
(or cursive l) and the two
4
angles (example: 2 and 4).
l
the two angles are
congruent, corresponding
2
2  4, CA, l ǁ k
angles (CA), so line l is
parallel to line k.
*Note: these pair of angles can go in any of the four directions (in pairs) from the two vertices Q and P
11/29 homework (#42)
Construct eight parallel line pairs, given a line and a point off the line. Make
two each by constructing congruent angles for each pair of corresponding angles
(CA's) from each of the four directions from the vertex (upper right, lower
right, lower left, upper left). Make congruence statements for each. EC:
construct a set of three parallel lines using CA's.
11/30 homework (#43) See steps on last pages
Construct four parallel line pairs, given a line and a point off the line. Make
four by constructing congruent angles for each pair of Alternate Exterior Angles
(AEA's) - doing both the obtuse and acute angles (two times each). Make
congruence statements for each construction.
12/2 homework (#44)
Construct eight parallel line pairs, given a line and a point off the line. Make
four by constructing congruent angles for each pair of Alternate Interior Angles
(AIA's) - doing both the obtuse and acute angles (two times each). Make two by
constructing supplementary angles for each pair of Same Side Interior Angles
(SSIA's). Make two more by constructing a perpendicular transversal thru the
point and then a new line perpendicular to the transversal at the point. Make
construction statements for each.
12/3 homework (#45)
Find the measures for all the interior angles (three triangles, and one
quadrilateral) given a large triangle ABC, where AB=CB and two rays AF and CE
that bisect angles A and C and intersect at point D in the center of the triangle
and measure of angle CAB = 52 degrees. (see attachment for a figure of this
exercise)
WEEK 13 (assignment 45)
Find the measures of each angle:
Given: AB  CB and AF bisects A and CE bisects C, and AF and CE intersect at point D, and mCAB = 52º
B
Angle
1
1
2
3
4
2
E
3
5
5
F
6
8
4
D
6
7
7
8
9
9
10
10
11
A
13
11
12
C
12
13
Measure
Given a line and a point, construct a line through the point, parallel to the given line using Alternate Exterior Angles
1. Begin with point P and
2. Draw an transversal line
3. Center the compass at
4. Span the compass radius
line k.
through point P, intersecting
point Q and draw* an arc
to the distance between the
line k. Label the intersection
intersecting both lines.
two intersection points of the
point Q. Now construct an
Without changing the radius
first arc. Now center the
angle with vertex P,
of the compass, center it at
compass at the point where
congruent to one of the two
point P and draw another
the second arc intersects
exterior angles (1 or 2)
arc 180⁰ in the opposite
transversal line PQ. Mark the
at Q.
direction (make sure they
arc intersection point R.
both pass thru the
transversal).
R
P •
P •
Q
Q
•
1
5. Label the new line PR
k
2
R
P
(or cursive l) and the two
l
Q
•
1
2
Q
•
1
2
k
•
1
2
6. Box a statement to show
the two angles are
4
P •
angles (example: 2 and 4).
P •
congruent, corresponding
2  4, AEA, l ǁ k
angles (CA), so line l is
k
parallel to line k.
*Note: these pair of angles can be either the obtuse or acute angles (in pairs) from the two vertices Q and P
k