Download CONSTRUCTING CONGRUENT LINE SEGMENTS B C D 1. Given

NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT LINE SEGMENTS
Given:
Task: Construct a segment congruent to
1.
A
B
.
Directions:
a) Draw a new, longer segment with your straightedge.
b) Place an endpoint on the left side of the new segment and label it A'.
c) Place the point of the compass on A.
d) Stretch the compass, so the pencil is exactly on B.
e) Without changing the span of the compass, place the compass point
on A' and swing an arc, so it crosses the segment you drew.
f) The intersection of the segment and arc should be labeled B'.
2. Given: CD
D
C
Task: Construct a segment congruent to CD and label it C'D'.
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT LINE SEGMENTS
1.
Given:
Task: Construct a segment congruent to
B
A
.
Directions:
a) Draw a new, longer segment with your straightedge.
b) Place an endpoint on the left side of the new segment and label it A'.
c) Place the point of the compass on A.
d) Stretch the compass so that the pencil is exactly on B.
e) Without changing the span of the compass, place the compass point
on A' and swing an arc, so it crosses the segment you drew.
f) The intersection of the segment and arc should be labeled B'.
2. Given: CD
Task: Construct a segment congruent to CD and label it C'D'.
Learning Constructions - Day 2
D
C
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT LINE SEGMENTS
1.
Given:
Task: Construct a segment congruent to
A
B
.
Directions:
D
2. Given: CD
Task: Construct a segment congruent to CD, label it C'D'.
C
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT LINE SEGMENTS
1.
Given:
Task: Construct a segment congruent to
.
A
B
Directions:
D
2. Given: CD
Task: Construct a segment congruent to CD, label it C'D'.
Learning Constructions - Day 2
C
DATE: _________________________
NAME: ________________________________________________
CONSTRUCTING A PERPENDICULAR BISECTOR
3.
Given:
Task: Bisect
.
A
Directions:
4. Given: DE
Task: Bisect DE and label the point of intersection as F.
E
D
Learning Constructions - Day 2
B
DATE: _________________________
NAME: ________________________________________________
CONSTRUCTING A PERPENDICULAR BISECTOR
3. Given:
Task: Bisect
.
Directions:
a) Place your compass point on A and stretch the compass MORE
THAN halfway to point B, but not beyond B.
b) With this length, swing a large arc that will go BOTH above and
below
.
c) Without changing the span on the compass, place the compass point
on B and swing the arc again until the two arcs intersect both above
and below AB.
d) With your straightedge, connect the two points of intersection.
e) This new segment bisects
. Label the point where the new
segment and segment
intersect as C.
4. Given: DE
Task: Bisect DE and label the point of intersection as F.
E
D
Learning Constructions - Day 2
A
B
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PERPENDICULAR LINE FROM A POINT ON A LINE
5. Given: P is on line m.
Task: Construct a line through P perpendicular to line m.
Directions:
P
m
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PERPENDICULAR LINE FROM A POINT ON A LINE
5. Given: P is on line m.
Task: Construct a line through P perpendicular to line m.
Directions:
a) Place your compass point on P and sweep an arc (below the line)
of any size that crosses the line twice. You will be creating (at
least) a semicircle.
b) STRETCH THE COMPASS LARGER!
c) Place the compass point where the arc crossed the line on one side
and make a small arc below the line. (The small arc could be
above the line if you prefer.)
d) Without changing the span on the compass, place the compass point
where the arc crossed the line on the OTHER side and make
another arc. Your two small arcs should be crossing.
e) With your straightedge, connect the intersection of the two small
arcs to P.
P
m
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PERPENDICULAR LINE FROM A POINT OFF A LINE
6. Given: G is off a given line.
Task: Construct a line through G perpendicular to the given line.
Directions:
G
d
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PERPENDICULAR LINE FROM A POINT OFF A LINE
6. Given: G is off a given line.
Task: Construct a line through G perpendicular to the given line.
Directions:
a) Place your compass point on Point G and sweep an arc of any
size that crosses line d twice.
b) Place the compass point where the arc crossed the line on one side
and make an arc ON THE OPPOSITE SIDE OF LINE d.
c) Without changing the span on the compass, place the compass point
where the arc crossed the line on the OTHER side and make
another arc. Your two new arcs should be crossing on the opposite
sides of the line.
d) With your straightedge, connect the intersection of the two new arcs
to point G.
G
d
Learning Constructions - Day 2
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PARALLEL LINE FROM A POINT OFF A LINE
7. Given: P above line m.
Task: Construct a line through P parallel to line m.
Directions:
P
m
Learning Constructions - Day 3
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING A PARALLEL LINE FROM A POINT OFF A LINE
7. Given: P above line m.
Task: Construct a line through P parallel to line m.
Directions:
a) Draw a point on line m to the left of P and label it Q.
b) Place compass on Q and draw an arc through P that intersect line m.
to the right of Q and label the intersection R.
c) Using the same compass setting as the first arc, draw two more arcs:
one from P, the other from R.
d) Label the intersection of the two arcs S.
e) Draw
parallel to line m.
P
m
Learning Constructions - Day 3
NAME: ________________________________________________
DATE: _________________________
CONSTRUCT A PARALLEL SEGMENT THROUGH A POINT ON A SEGMENT
A
8. Given: AB and C on BD.
Task:
Construct a line parallel to AB through C.
Directions:
a) Copy
B
C
D
B using C as the vertex of the new angle.
W
9. Given: XW and Y on XZ.
Task: Construct a line parallel to XW through Y.
Learning Constructions - Day 3
X
Y
Z
NAME: ________________________________________________
DATE: _________________________
CONSTRUCT A PARALLEL SEGMENT THROUGH A POINT ON A SEGMENT
A
8. Given: AB and C on BD.
Task:
Construct a line parallel to AB through C.
C
B
D
Directions:
W
9. Given: XW and Y on XZ.
Task: Construct a line parallel to XW through Y.
Learning Constructions - Day 3
X
Y
Z
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT ANGLES
A
10. Given:
Task: Copy
A
Directions:
a) Using a straightedge, draw a ray. Label the left endpoint A'. ith
b) your
Placestraightedge.
the compass point on vertex A and swing an arc through
both rays of
A. Mark the top intersection B and the lower C.
c) Without changing the span of the compass, place the compass point on
A' and swing the same arc. Mark the intersection C'.
d) Place the compass point on B and open it to C.
e) Without changing the span of the compass, place it on C' and swing
an arc which intersects the first arc. Mark this B'
f) Draw a ray from A' thru B'.
F
11. Given:
Task: Copy
A
F
F
Learning Constructions - Day 4
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT ANGLES
A
10. Given:
Task: Copy
A
Directions:
a) Using a straightedge, draw a ray. Label the left endpoint A'. ith
b) Place the compass point on vertex A and swing an arc through
both rays of
A. Mark the top intersection B and the lower C.
c) Without changing the span of the compass, place the compass point on
A' and swing the same arc. Mark the intersection C'.
d) Place the compass point on B and open it to C.
e) Without changing the span of the compass, place it on C' and swing
an arc which intersects the first arc. Mark this B'
f) Draw a ray from A' thru B'.
11. Given: F
Task: Copy
F
Learning Constructions - Day 4
A
F
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT ANGLES
A
10. Given:
Task: Copy
A
Directions:
A
F
11. Given:
Task: Copy
F
F
Learning Constructions - Day 4
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING CONGRUENT ANGLES
10.
Given:
A
Task Copy
A
Directions:
A
F
11. Given:
Task: Copy
F
Learning Constructions - Day 4
F
DATE: _________________________
NAME: ________________________________________________
CONSTRUCTING AN ANGLE BISECTOR
12.
Given:
A
Task: Bisect
A
Directions:
a) Place the point of the compass on vertex A.
b) Draw an arc which intersects both rays of A. Mark the upper
intersection B and the lower C.
c) Place the compass point on B and swing an arc in the interior of
the angle.
d) Now, place the compass point on C and swing the same arc in
the interior of the angle so that it intersects the first arc.
e) Draw a line from vertex A through the point where the arcs
intersect in the angle's interior.
A
Learning Constructions - Day 4
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN ANGLE BISECTOR
A
12. Given:
Task: Bisect
A
Directions:
a) Place the point of the compass on vertex A.
b) Draw an arc which intersects both rays of A. Mark the upper
intersection B and the lower C.
c) Place the compass point on B and swing an arc in the interior of
the angle.
d) Now, place the compass point on C and swing the same arc in
the interior of the angle so that it intersects the first arc.
e) Draw a line from vertex A through the point where the arcs
intersect in the angle's interior.
Learning Constructions - Day 4
A
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN ANGLE BISECTOR
A
12. Given:
Task: Bisect
A
Directions:
A
Learning Constructions - Day 4
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN ANGLE BISECTOR
A
12. Given:
Task: Bisect
A
Directions:
A
Learning Constructions - Day 4
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING "n" CONGRUENT SEGMENTS
Given:
13.
Task:
Divide
into five congruent segments.
Directions:
A
B
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED EQUILATERAL TRIANGLE
Given: Circle F
14.
Task:
Create an inscribed equilateral triangle.
Directions:
F
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING "n" CONGRUENT SEGMENTS
13.
Given:
Task:
Divide
into five congruent segments.
Directions:
a) Opening at an upward acute angle, draw a long segment from endpoint A.
b) Set the compass at a narrow opening so "n" [5 for this example]
segments can be created. Mark and label the points C, D, E, F & G.
c) Opening at a downward acute angle, draw a long segment from endpoint
B. Use the same compass setting to mark "n" segments [5 on this line].
d) Label the points created H, I, J, K & L.
e) Connect the "n" arc markings on the segments above and below the
original line: G to B, F to H, E to I, D to J, C to K, and A to L. There
will be "n" congruent segments created by the connecting lines
intersecting the original line.
A
B
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED EQUILATERAL TRIANGLE
14.
Given: Circle F
Task: Create an inscribed equilateral triangle.
Directions:
a) Set a compass to the length of the circle F radius.
b) Using the intersection of the diameter and the circle, create a new
circle with the same radius.
c) The two circles will interesect at two points. Set your compass to
distance between these two points.
d) With the compass point on one of the points of intersection, swing
a small arc to mark a new intersection to circle F.
e) Connect the three intersections of circle F to form an equilateral
triangle.
Learning Constructions - Day 5
F
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED REGULAR HEXAGON
15.
Given: Circle G
Task: Create an inscribed regular hexagon.
Directions:
G
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED REGULAR PENTAGON
16.
Given: Circle J
Task: Create an inscribed regular pentagon.
Directions:
J
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED REGULAR HEXAGON
15.
Given: Circle G
Task: Create an inscribed regular hexagon.
Directions:
a) Set a compass to the length of the radius of
circle G. This will be the length of each side
of the hexagon.
b) Using this setting, place your compass on the
left intersection of the circle and its diameter
and swing two intersecting arcs, one above
and one below the circle's diameter.
c) Repeat step "b)" with your compass
point on the right intersection of the
circle and its diameter.
d) Connect the six points.
G
Learning Constructions - Day 5
NAME: ________________________________________________
DATE: _________________________
CONSTRUCTING AN INSCRIBED REGULAR PENTAGON
16.
Given: Circle J
Task: Create an inscribed regular pentagon.
Directions:
a) Draw a diameter of the circle through the center point and mark
its endpoints C and M. [Note: It does not have to be vertical.]
b) Construct a ray perpendicular to CM at point O.
c) Mark the point S where it crosses the circle.
d) Find the midpoint of SO by constructing its perpendicular
bisector. Label the midpoint L.
e) Set the compass on L, adjust its width to S or O and draw a circle.
f) Draw a line from M through L, so it crosses the small circle in
two places. Label the closer to M intersection P and further N.
g) Set the compass on M and adjust its width to P.
h) Draw a broad arc that crosses the given circle in two places.
Label them A and E.
i) Set the compass on M and adjust its width to N.
j) Draw a broad arc that crosses the given circle in two places.
Label the points B and D.
k) Draw a line from A to B, then B to C, etc. until you have drawn all
five sides of the pentagon.
Learning Constructions - Day 5
O