Construct a Triangle given SAS

If you are given two sides and the included angle for a triangle, you can construct it by making a copy of one of the sides, copying the angle with its vertex at an endpoint of the side, then marking off the length of the other side, and finally constructing the third side.

Given:  Sides AB and AC, and angle A, construct triangle ABC:

Solution:

Draw a segment longer than AB, label one endpoint as A, and use the compass with its radius set to the length of AB to mark off point B:

 

 

Then construct a copy of angle A at the endpoint A:

Next mark off point C using AC as the radius of the compass and point A as the center.

Finally construct side BC by placing the straight-edge at points B and C:

Here is a an animation of this construction.

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