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Remember
-- use your compass and straight edge only! |
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A reference
line is a line upon which you produce copies of existing figures.
Given:
Line segment AB
Task: To construct a line segment congruent to line segment AB.
Directions:
1. If a reference line does not already exist, draw a reference line
with your straightedge upon which you
will make your construction. Place a starting point on the reference
line.
2. Place the point of the compass on point A.
3. Stretch the compass so that the pencil is exactly on B.
4. Without changing the span of the compass, place the compass point
on the starting point on the reference line and swing the pencil so that it crosses the reference
line. Label your copy.
Your copy and
line segment AB are congruent (equal in length).
Explanation
of construction:
The two line segments are
the same length, therefore they are congruent.
Given:
angle BAC
Task: To construct an angle congruent to angle BAC.
Directions:
1.
If a reference line does not already exist, draw a reference line
with your straightedge upon which you
will make your construction. Place a starting point on the reference
line.
2. Place the point of the compass on the vertex of angle BAC
(point A).
3. Stretch the compass to any length so long as it stays ON the
angle.
4. Swing an arc with the pencil that crosses both sides of angle
BAC.
5. Without
changing the span of the compass, place the compass point on the starting
point of the reference line and
swing an arc that will intersect the reference line and go above the
reference line.
6. Go back to angle BAC and measure the width (span) of the arc from where
it crosses one side of the angle to where it crosses the other side of the
angle.
7. With this width, place the compass point on the reference line
where your new arc crosses the reference line and mark off this width on your new arc.
8. Connect this new intersection point to the starting point on the
reference line.
Your new angle is congruent to angle
BAC.
Explanation of
construction:
When this
construction is finished, draw a line segment connecting where the arcs
cross the sides of the angles. You now have two triangles that have 3 sets of
congruent (equal) sides. SSS is sufficient to prove triangles
congruent. Since the triangles are congruent, any leftover
corresponding parts are also congruent - thus, the angle on the reference
line and angle BAC are
congruent.
Click here to learn how to
Bisect an Angle and Line Segment
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