Name:
3_Skill Set
Date:
Duplicating a Segment
Stage 1
Stage 2
Stage 3
Step 1
The complete construction for copying a segment,
Describe each stage of the process.
Step 2
Use a ruler to measure
Step 3
Describe how to duplicate a segment using patty paper instead of a compass.
and
, is shown above.
. How do the two segments compare?
Duplicating an Angle
Step 1
The first two stages for copying DEF are shown below.
Describe each stage of the process.
Stage 1
Stage 2
Step 2
What will be the final stage of the construction?
Step 3
Use a protractor to measure
about these angles?
Step 4
Describe how to duplicate an angle using patty paper instead of a
compass
DEF and
G. What can you state
Name:
3_Skill Set
Date:
Construct Perpendicular Bisector
Step 1 : Stretch your compasses until it is more then half the length of AB. Put the sharp end at A
and mark an arc above and another arc below line segment AB.
Step 2 : Without changing the width of the compasses, put the sharp end at B and mark arcs
above and below the line segment AB that will intersect with the arcs drawn in step 1.
Name:
3_Skill Set
Step 3 : Join the two points where the arcs intersect with a straight line. This line is the
perpendicular bisector of AB. P is the midpoint of AB.
Date:
Name:
3_Skill Set
Construct Angle Bisector
Given. An angle to bisect. For this example, angle ABC.
Step 1. Draw an arc that is centered at the vertex of the angle. This arc
can have a radius of any length. However, it must intersect both sides
of the angle. We will call these intersection points P and Q This
provides a point on each line that is an equal distance from the vertex
of the angle.
Step 2. Draw two more arcs. The first arc must be centered on one of
the two points P or Q. It can have any length radius. The second arc
must be centered on whichever point (P or Q) you did NOT choose for
the first arc. The radius for the second arc MUST be the same as the
first arc. Make sure you make the arcs long enough so that these two
arcs intersect in at least one point. We will call this intersection point
X. Every intersection point between these arcs (there can be at most
2) will lie on the angle bisector.
Step 3. Draw a line that contains both the vertex and X. Since the
intersection points and the vertex all lie on the angle bisector, we
know that the line which passes through these points must be the
angle bisector.
Date:
Name:
3_Skill Set
Date:
Slope of parallel or perpendicular lines
Consider A(–15, –6),
B(6, 8), C(4, –2),
and D(– 4, 10). Are
and
parallel,
perpendicular, or
neither?
Solution
Calculate the slope of each line.
8 – (–6)
2
slope of
= 6 – (–
15)
The slopes, and
EXAMPLE
B
Solution
10 – (–2)
=
slope of
3
, are negative reciprocals of each other, so
=
3
=–
–4–4
2
.
Given points E(–3, 0), F(5, –4),
and Q(4, 2), find the coordinates
of a point P such that
is
parallel to
.
We know that if
||
, then
the slope of
equals the slope
of
. First find the slope of
.
–4–0
=
slope of
–4
1
=
5– (– 3)
=–
8
2
There are many possible ordered pairs (x, y) for P. Use (x, y) as the coordinates of P,
and the given coordinates of Q, in the slope formula to get
2–y
1
=–
4–x
2
Now you can treat the denominators and numerators as separate equations.
4–x=2
2 – y = –1
– x = –2
– y = –3
x=2
y=3
Thus one possibility is P (2, 3). How could you find another ordered pair for P? Here’s a hint: How
many different ways can you express –
?