Lesson 1: Angles - Replicating Angles with a Compass and Ruler

   Constructing Knowledge

At times, you may be required to replicate an angle. A replica is an exact copy. To replicate an object means to make another object that is the same as the first.

A second method for replicating angles uses a compass and a ruler.

Step 1: Draw a horizontal line with a ruler. Mark the vertex.

Step 2: Put the point of the compass on the vertex of the original angle, and draw a large arc cutting through both arms of the angle.

Step 3: Without moving the legs of the compass, make an identical arc starting from the vertex mark on the horizontal line your drew.

Step 4: Go back to the original angle, and put the compass point where the arc intersects the horizontal arm of the angle. Open the compass as wide as the position where the pencil touches exactly where the arc intersects the second angle arm.

Step 5: On the new angle, keeping the compass legs in the same place, put the compass point on the horizontal line that intersects the first arc you drew. Draw a small arc overlapping the arc that is already there.

Step 6: Connect the vertex mark and the point where the two arcs intersect.

   Multimedia

A video showing how to replicate an angle with a compass is provided.


EXAMPLE

Replicate the following angle using a protractor and a ruler.



Solution


Step 1: Draw a horizontal line with a ruler. Mark the vertex.



Step 2: Put the point of the compass on the vertex of the original angle, and draw a large arc cutting through both arms of the angle.



Step 3: Without moving the legs of the compass, make an identical arc starting from the vertex mark on the horizontal line your drew.



Step 4: Go back to the original angle, and put the compass point where the arc intersects the horizontal arm of the angle. Open the compass as wide as the position where the pencil touches exactly where the arc intersects the second angle arm.



Step 5: On the new angle, keeping the compass legs in the same place, put the compass point on the horizontal line that intersects the first arc you drew. Draw a small arc overlapping the arc that is already there.



Step 6: Connect the vertex mark and the point where the two arcs intersect.



The original angle is now replicated.


Now, it is your turn! Complete the questions in your Chapter 6, Lesson 1 Practice Makes Perfect that refer to Replicating Angles with a Compass and Ruler.



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