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(Name)

_______________ (Period)

compass &

straightedge

CONSTRUCTION

MANUAL

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Congruent Segment 1. Using a straightedge, draw a line. Place a point on this

line, name it C. 2. Set your compass to the length of segment AB. 3. Place the compass on point C and make a small arc on

the line. Label the arc intersection D. 4. Place tick marks to show AB CD .

A

B

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Perpendicular Bisector and Midpoint 1. Open the compass so that it is more than half of the

segment length. 2. Place the compass point on one endpoint and make a

large arc (like a semi-circle). 3. Using the same compass setting, repeat Step 2 from

the other endpoint. 4. Using a straight edge draw a line through the

intersection of these 2 arcs. 5. Label the midpoint M, place tick marks on congruent

segments and a box to show perpendicular.

A

B

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Circumscribed Circle 1. Construct the perpendicular bisector for each side of the

triangle. 2. All 3 perpendicular bisectors should be concurrent at the

circumcenter. 3. Using a compass, draw the circumscribed circle. Use

the circumcenter as the center and open the compass enough to reach a vertex of the triangle.

4. Label the circumcenter C.

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Angle Bisector 1. Place the compass point on the vertex of the angle and

open the compass. 2. Make an arc that intersects both sides of the angle.

Mark these points A and B. 3. Place the compass on point A and make an arc inside

the angle. 4. Without changing the compass setting, place the

compass on point B and make another arc so that it crosses the arc made from point A. Label this point C.

5. Using a straightedge draw a ray from the vertex of the angle through point C.

6. Place tick marks on congruent angles.

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Inscribed Circle 1. Construct the angle bisector for each angle of the

triangle. 2. All 3 angle bisectors should be concurrent at the

incenter. Label the incenter I. 3. Using a compass, draw the inscribed circle. Use the

incenter as the center and open the compass enough to reach a side of the triangle.

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Congruent Triangle 1. Using a straightedge, draw a line, place a point on the

line and label it M. 2. Set your compass equal to the distance of AB. Place

the point of your compass on M and draw an arc that intersects the line. Label the intersection N.

3. Set your compass equal to the distance of AC. Place your compass on M and make and arc.

4. Set your compass equal to the distance of BC. Place your compass on N and draw an arc that intersects the arc you just made. Label the intersection point O.

5. Connect points M, N, and O. Place tick marks to show congruent segments. ABC MNO .

C

B A

C

B A

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Congruent Angle 1. Draw a ray with endpoint D. 2. Place the compass on point A and draw an arc across

both sides of the angle. Label the intersections B and C.

3. Using the same compass setting, place the compass on point D and draw a long arc crossing the ray. Label the intersection E.

4. Set the compass to the distance of B to C. Place the point of the compass on E and draw an intersecting arc. Label the intersection point F.

5. Using a straightedge draw a ray from point D through point F.

6. Place tick marks to show congruent angles. BAC FDE .

A

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Perpendicular line through a point 1. Place the point of your compass on point P and draw

an arc that intersects the line twice. Label these intersections A and B.

2. Place the point of your compass on point A and draw an arc on the opposite side of the line from point P.

3. Using the same compass setting, place the point of your compass on point B draw an arc that intersect on the opposite side of the line from point P. Label the intersection of these arcs C.

4. Use a straightedge to draw a line through points P and C.

5. Place the right angle symbol to show: CP AB

P

P

P

P

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Parallel line through a point 1. Using a straight edge draw a line through point P and

line k. Label the intersection point V. 2. Place the point of the compass on point V and draw an

arc that intersects point P and line k. Label the intersection of the arc and line k point B.

3. Using the same compass setting, place the point of the compass on point P and draw an arc on the interior of

PVB . 4. Using the same compass setting, place the point of the

compass on point B and draw an arc on the interior ofPVB . Label the intersection of these arcs point D.

5. Using a straightedge draw PD .

6. Place arrows to show:

P

P

P

P k

k

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Reflection 1. To construct a reflection, one must construction

perpendicular lines through points. NOTE: If you can reflect a point, then you can reflect a figure. HINT: It is helpful to use a different color pencil for each point you reflect.

2. Select the point you are reflecting, Place the point of your compass on the point and draw and arc that intersect the line of reflection twice. (ARC 1) Darken those intersection points.

3. Using the same compass setting, Place the point of the compass on one of those intersections and swing and arc on the opposite side of the line as the original point. (ARC 2)

4. Using the same compass setting, repeat step 3 from the other intersection point. (ARC 3) “x” marks the spot. The intersection of arc 2 & 3 is the image of the original point. Label accordingly: 'P P

5. Using a straightedge connect 'PP , use markings to show the perpendicular lines and congruent segments.

6. REPEAT steps 2-5 for each point. Use a straightedge to connect figure as needed.

P B

A

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Reflect each figure.

A

B

C D

J

K

T

H

G

F

E

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Rotation 1. To construct a rotation, one must construction

congruent angles. NOTE: If you can rotate a point, then you can rotate a figure. HINT: It is helpful to use a different color pencil for each point you rotate.

2. Select the point to be rotate. Place the point of the compass on the center of rotation and open your compass to the point to be rotated. Use your compass to draw an “orbit” or “path” for this point. (ARC 1)

3. Using the same compass setting, place the point of the compass on the vertex of the angle of rotation. Draw an arc from ray to ray. (ARC 2) Darken the 2 points of intersection.

4. Set your compass to the distance between the darken points of arc 2. Use this compass setting, place the point of the compass on the original point and draw an arc that intersects arc 1. (ARC 3)

5. “x” marks the spot. The intersection of arc 1 & 3 is the image of the original point. Label accordingly: 'P P

6. REPEAT steps 2-5 for each point. Use a straightedge to connect figure as needed.

P

Center of Rotation

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P

B

A

Center of Rotation

S

T

I

W

T

Rotate each figure.

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Translation 1. To construct a translation, one must construction

parallel lines through points. NOTE: If you can translate a point, then you can translate a figure. HINT: It is helpful to use a different color pencil for each point you translate.

2. From each point, construct a line parallel to the translation vector. a. Plot a point on the translation vector. Label this point V. (It might

be necessary extend the translation vector with a straightedge.) b. Place the point of your compass on point V and open it to the point

you are translating. From this point draw an arc that intersects the vector. (ARC 1) Label intersection point D.

c. “x” marks the spot. Using the same compass setting as arc 1, place the point of the compass on the original point and swing an arc, (ARC 2) repeat by placing the compass on point D and swing an arc that intersects arc 2. (ARC 3)

d. Use a straightedge to draw a line through the original point and the intersection of arc 2 & arc 3.

e. REPEAT steps b-d for each point.

3. Use the compass to measure the length of the translation vector. Then use the compass to translate each point that amount. Label accordingly: 'P P

4. Use a straightedge to connect figure as needed.

P

K

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Translate each figure.

A

B

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Construct a figure congruent to each figure below. Place tick marks.

Construct an inscribed circle. Construct a circumscribed circle. Label the incenter I. Label the circumcenter C.

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Remember to complete the construction include proper markings.

Construct the angle bisector. Construct the perpendicular bisector. Label the midpoint M.

Construct a parallel line through the given point. Construct a perpendicular line through the given point.

P P

P

P

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Reflect the figure.

C

F

L

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Rotate the figure.

P

R

T

o

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Translate the figure.

N

R

T