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Construction is an ancient method of duplicating a geometric figure using only a straightedge and a compass. If you begin with any chosen triangle, you can construct a congruent copy of it if you match any two sides and the angle between them. This is called the “SideAngleSide,” or SAS, Criterion. You can accomplish the same task using a protractor and ruler. This is easier but is not strictly a construction.
Steps
Part 1
Part 1 of 4:Constructing the First Side

1Set your compass to the length of a chosen side. Begin with a chosen triangle with points labeled , , and . Set one point of your compass on point , and open your compass so the pencil is on point . Fix your compass so this measurement is set.^{[1] X Research source }
 Some compasses are more flexible than others. When you set this length, you need to be sure that the compass does not move as you transfer to your new figure. There may be a screw to tighten or a clip to adjust to set this length.

2Copy the length. At a new position on your paper, wherever you wish to draw the new triangle, mark a point and label it . Set the point of your compass on . Mark a point with the compass pencil at the designated length. Label this point .^{[2] X Research source }Advertisement

3Connect the points. Use your straightedge to connect points and . This line should be an exact copy of side from the original triangle. ^{[3] X Research source }
 If segment does not look like it is the same length as original side , then your compass probably slipped while you were moving it. Start over and try again.
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Part 2
Part 2 of 4:Constructing the Angle

1Choose any compass setting. To begin copying the angle, set your compass to any reasonable size. Choose a setting that is roughly half the length of the sides of your original triangle. ^{[4] X Research source }

2Draw arcs around point A. Set the point of your compass on point of the original triangle. Swing the compass so it draws an arc that intersects both sides and .^{[5] X Research source }
 Mark the two positions where the arc intersects the triangle sides. Label the intersection with side as and label the intersection with side as .

3Copy the arc onto the new triangle construction. Without letting the compass setting change, place the point of the compass on of your construction. Draw an arc that intersects side and continues about as long as the arc you drew on the original triangle. ^{[6] X Research source }
 Mark the position where the arc intersects side as .

4Set the compass to the angle width. Pick up the compass and set the point on point on the original triangle. Set the width of the compass by placing the pencil tip on .^{[7] X Research source }

5Copy the angle width to the new construction. Position your compass so the point is on . Draw a small arc that intersects the arc that you previously drew. Mark the point where these two arcs intersect as .^{[8] X Research source }

6Complete the angle. Using your straightedge, draw a line that connects points and . Extend the line beyond so it will be slightly longer than side of your original triangle.
 This angle, should be an exact duplicate of angle of the original triangle. If it doesn’t look the same, you should repeat the process and make sure that your compass does not slip during the transfers.
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Part 3
Part 3 of 4:Finishing the Triangle

1Set your compass to the length of AC. Place the tip of the compass on point . Place the pencil tip on point . Set the length of the compass so it does not shift. ^{[9] X Research source }

2Transfer the length to your construction. Move the tip of the compass to point of the construction. Using the compass pencil, draw a small arc that intersects the extended line that you previously constructed. Mark the point of intersection as .^{[10] X Research source }
 The length of should be the same as the length of . If not, then try again.

3Connect points and . Using your straightedge, connect points and on your construction. This should finish triangle as an exact copy of triangle .^{[11] X Research source }
 If you wish, you can clean up your construction by erasing the arc lines that you drew for the construction.
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Part 4
Part 4 of 4:Constructing a Triangle With a Protractor and Ruler

1Measure side . You can also construct a duplicate triangle, using two given sides and the angle between them (SAS), using a ruler and protractor. This is not the true classical method, but it is easier if you are allowed to use these extra tools. Use your ruler to measure the length of side .

2Copy the side length to the new construction. At a new position on your paper, where you want to draw your new triangle, mark a point . Set your ruler at point and draw a line segment that is the same length as side . Label the end of this line segment .

3Copy angle BAC. On the original triangle, measure angle with your protractor. Lift the protractor and set the center point on point of the new construction. Mark an angle the same size as angle . Use your straightedge to connect and this mark. Extend the line slightly longer than the length of side of the original triangle.

4Measure side . Using the ruler, measure the length of side of the original triangle.

5Copy the side length to the new construction. Place one end of the ruler at point . Along the line that you drew in the previous step, mark a length equal to the measured length of side . Label the end of this length .

6Complete the triangle. Connect points and as a congruent copy of triangle .
 If you wish, you can erase the markings that you made during the construction.
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Community Q&A

QuestionWhich line do I use as base?DonaganTop AnswererAny side of a triangle may be considered its base. Choose the side most convenient for your purposes.
Video
Tips
Things You'll Need
 Paper
 Pen or Pencil
 Protractor
 Compass
 Ruler
References
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