Transcript E6 recognize, name, describe, and represent perpendicular lines

E6 Students will be expected to
recognize, name, describe, and
represent perpendicular
lines/segments, bisectors of angles
and segments, and perpendicularbisectors of segments.
What are the characteristics
of a ‘line’ in geometry?
A line is straight and extends in
both directions forever. It has no
definite endpoints.
What defines a ‘line segment’ in
geometry?
A
B
A line segment is straight and
has two definite endpoints. This
is line segment AB or BA.
What are perpendicular lines?
Where do we see perpendicular
lines in the real world?
Student Activities
How can you use a mira to draw perpendicular
lines?
 Draw a line segment and place the mira across
it, moving the mira until the image of the part
of the segment on one side of the mira falls on
the segment on the other side. The line on
which the mira sits is perpendicular to the
original line; therefore, place a pencil against
the beveled edge of the mira and draw in this
perpendicular.

What does ‘bisect’ mean?
‘Bisect’ means to divide in half.
What can be bisected in geometry?
Line segments and angles can be
bisected.
A perpendicular-bisector is a line segment that
cuts through a second segment or line forming
right angles. It also cuts the segment in half or
bisects it.
Try to use your mira to show a perpendicularbisector.

Explanation: When the image of the endpoint
of the segment falls on the other endpoint,
the mira is bisecting the segment; therefore,
the line on which the mira sits would be the
perpendicular-bisector of the segment.
What are parallel lines?
Where do we see parallel lines in
the real world?
Use two straws to make the following
arrangements:









parallel to one another
intersecting
perpendicular at an end point of one straw
perpendicular at endpoints of each straw
one straw perpendicular to the other straw at its midpoint
one straw bisecting the other straw but not perpendicular
each straw bisecting the other straw but not perpendicular
one straw bisected by the other straw and perpendicular
each straw bisecting the other straw and perpendicular
Bisecting Angles Using
Three Methods
Bisect the first angle given to you by folding
one arm onto the other.
 Bisect the next angle by using a mira to find
where one arm would reflect onto the other
when it is placed through the vertex
 Bisect the third angle by using a protractor
to measure the angle. Then bisect it.
 Practise the three methods by bisecting the
other angles on the sheet provided to you.
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E6.1 Draw a right angle, an acute
angle, and an obtuse angle. Use only a
mira to draw in the bisector of each
angle. Check your results by paper
folding and by measuring the angles
with a protractor.

E6.2 Use the capital letters of the
alphabet that use only segments.
Find examples of bisectors of
segments, perpendicular segments,
and perpendicular-bisectors. Share
your findings.

E6.3
Draw, without measuring, a
segment that is approximately 10cm
long. Next, construct a perpendicular
bisector of this segment, using only a
mira.

E6.4 Fold sheets of paper in half and
then in half again. Open them up to
reveal the folds and draw in segments
along these folds. Describe the
relationship
between
these
two
segments.