Constructions

To construct a line segment congruent to a given line

segment.1. Construct a line, label two points A and B.

A B

2. Place your compass point on Point A.3. Open the compass until the pencil end touches Point B, strike an arc.

DO NOT CHANGE THE COMPASS SETTING4. Draw a line, longer than your original line and label a point on that line, point C.

C

5. Place your compass point on the point and strike an arc that intersects the line. Label that point D.

D

AB CD

To Bisect a given Line Segment and create a Line Perpendicular to a Given

Line.1. Construct a line, label two points A and B.

A B

2. With the compass point on point A, open the compass larger than halfway to B but not all the way to B. Strike a large arc above line segment AB

and now construct another large arc below line segment AB.

3. With the compass point on B, strike an arc that intersects the arc that you just made above line segment AB from point A, label that point C.

C

4. Strike another arc below line segment AB that intersects the arc, label that point D.

D

5. Connect points C and D.5. Label the point where segment CD intersects AB, point E.

E

AEEB, CEED,

and ABCD

To construct an Equilateral Triangle that is NOT Inscribed in a Circle1. Construct a line segment, label the endpoints X and Y.

X Y

2. Open your compass the distance of X to Y.

DO NOT CHANGE THE COMPASS SETTING

3. Place the compass on X and strike a LARGE arc above line segment XY.5. Connect points X to Z and Y to Z.

4. Place the compass point on Y and strike another large arc above line segment XY, this arc should intersect the arc from step #3. Label that point Z.

Z

YX XZ YZ

To construct a perpendicular line through a given point on the line

1. Construct a line...

2. Label a point on the line A.

A

3. Place your compass point on A and strike an arc that intersects the line two times.

X Y

4. Label these points X and Y.5. Open the compass a little more then place it on X.

6. Strike an arc above the line.

7. Place the compass point on Y and strike an arc that intersects the one you just made.

Do not change the compass setting

8. Label the intersection point Z.

Z

9. Connect point Z to A.

To construct an angle congruent to a given angle

1. Construct an acute angle, label the vertex A

A

2. Draw a line and label a point on the line D.

D

3. Place your compass point on A and strike an arc that intersects both rays of the angle.

DO NOT CHANGE THE

COMPASS SETTING

4. Label the intersections B and C

B

C

5. Place the compass point on D and strike an arc,

label the point where the arc intersects the line point E.

E

6. Place the compass point on B and close the

compass until the pencil tip touches C, strike an arc.

DO NOT CHANGE THE

COMPASS SETTING

7. Place the compass point on E and strike an arc that

intersects the previous arc. Label that point F.

F

8. Connect points D and F.

BAC FDE

To construct a hexagon inscribed in a circle

1. Construct a circle.

DO NOT CHANGE YOUR COMPASS SETTING!2. Make a mark on the edge of your circle. Label that point A

A

3. Place the compass point on A and strike a small arc that intersects the edge of your circle. Label that point B.

B

5. Place the compass point on C and strike a small arc that intersects the edge of your circle. Label that point D.

C

4. Place the compass point on B and strike a small arc that intersects the edge of your circle. Label that point C.

D

6. Place the compass point on D and strike an arc that intersects the edge of your circle, label that point E.

7. Place the compass point on E and strike an arc that intersects the edge of your circle, label that point F.

E

F

8. Connect points A to B, B to C, C to D, D to E, E to F and F to A.

To construct a hexagon inscribed in a circle

1. Construct a circle.

DO NOT CHANGE YOUR COMPASS SETTING!2. Make a mark on the edge of your circle. Label that point A

A

3. Place the compass point on A and strike a small arc that intersects the edge of your circle. Label that point B.

B

5. Place the compass point on C and strike a small arc that intersects the edge of your circle. Label that point D.

C

4. Place the compass point on B and strike a small arc that intersects the edge of your circle. Label that point C.

D

6. Place the compass point on D and strike an arc that intersects the edge of your circle, label that point E.

7. Place the compass point on E and strike an arc that intersects the edge of your circle, label that point F.

E

F

8. Connect points A to B, B to C, C to D, D to E, E to F and F to A.8. Connect points A to C, C to E, E to A.

To construct a square inscribed in a circle

1. Construct a circle, label the center O.

O

2. Draw a diameter for Circle O, label the points where they intersect the circle A and B.

A B

3. Bisect line segment AB (see notes on bisecting a line). Label the where this line intersects the circle C and D.

C

D

4. Connect A to C, A to D, B to C and B to D.

To construct a hexagon With Triangles and Quadrilaterals

1. Construct a circle.

DO NOT CHANGE YOUR COMPASS SETTING!2. Make a mark on the edge of your circle. Label that point A3. Place the compass point on A and strike a small arc that intersects the edge of your circle. Label that point B.

B

5. Place the compass point on C and strike a small arc that intersects the edge of your circle. Label that point D.

C

4. Place the compass point on B and strike a small arc that intersects the edge of your circle. Label that point C.

D

6. Place the compass point on D and strike an arc that intersects the edge of your circle, label that point E.

7. Place the compass point on E and strike an arc that intersects the edge of your circle, label that point F.

E

F

8. Connect points A to B, B to C, C to D, D to E, E to F and F to A.9. Connect points A to C, C to E, C to D, D and E to A. Then connect B to D, D to F and F to B.

A