Compass And Straightedge Construction

Of Parallel Lines

Figure 1.


1. Draw a straight line using a ruler on a piece of paper from edge to edge. Call this line l . Label point U on line l   close to the left edge of the paper, but not to close.

Proof A.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 2.


2. With a compass mark and then label point A on line l   at the distance a away from point U.

Proof B.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 3.


3. Keep marking points distance a away from the last point drawn and label them B, C, D, E, F, G, and V respectively.

Proof C.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 4.


4. Take a compass and draw a circle with the center at point B and make the radius larger than distance a.

Proof D.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 5.


5. Don’t change the distance on the compass and put the point of the compass on point U and draw an arc that intersects the first circle at at points P1 and P2.

Proof E.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 6.


6. Use your ruler and draw a long line through where the arcs intersect at points P1 and P2 then label this line k  .

Now erase the circle and arc and the labels P1 and P2.

Proof F.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 7.


7. On line k   , use your compass to mark then label points H, I, J, K, L, M, and N respectively at the distance a away from each other starting at point A.

Proof G.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 8.


8. Use your compass and at point M on line k   draw a perpendicular line to line k   the label this line m   .

Proof H.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 9.


9. Measure and mark six distances of a units apart on line m   with your compass.

Label these points R, S, T, U, V, and W respectively.

Proof I.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 10.


10. Draw a line from W to G and label this line n   then mark points X, Y, Z, N, and O respectively at the distance a away from each other and label them.

Proof J.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN

Figure 11.


11. Connect the points on line n to the points on line k respectively (X to L, Y to K…) and the points on line m and the points on line l and connect the points respectively (R to B, S to C…).

Proof K.

   
# Statements Reasons
1 abcdefg GIVEN
2 abcdefg GIVEN





Perpendicular Lines to Given Paraqllel Lines

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