E6 Students will be expected to recognize, name, describe, and represent perpendicular lines/segments, bisectors of angles and segments, and perpendicular-bisectors of segments. - PowerPoint PPT Presentation

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E6 Students will be expected to recognize, name, describe, and represent perpendicular lines/segments, bisectors of angles and segments, and perpendicular-bisectors of segments.

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Title: E6 Students will be expected to recognize, name, describe, and represent perpendicular lines/segments, bisectors of angles and segments, and perpendicular-bisectors of segments.


1
E6 Students will be expected to recognize, name,
describe, and represent perpendicular
lines/segments, bisectors of angles and segments,
and perpendicular-bisectors of segments.  
2
What are the characteristics of a line in
geometry?
A line is straight and extends in both directions
forever. It has no definite endpoints.
3
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4
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.
5
What are perpendicular lines?
Where do we see perpendicular lines in the real
world?
6
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7
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.

8
What does bisect mean?
Bisect means to divide in half.
What can be bisected in geometry?
Line segments and angles can be bisected.
9
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
perpendicular-bisector.
  • 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.

10
What are parallel lines?
Where do we see parallel lines in the real world?
11
(No Transcript)
12
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

13
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.
  •  

14
  • 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.

15
  • 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.

16
  • E6.3 Draw, without measuring, a segment that is
    approximately 10cm long. Next, construct a
    perpendicular bisector of this segment, using
    only a mira.

17
  • 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.
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