Constructing an isosceles triangle given a side and apex angle

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After doing this Your work should look like this
Start with a angle BAC and line segment FG. The length FG will be the side lengths of the triangle and BAC will be the angle at the top (apex) of the triangle.
In Steps 1-8 we copy the apex angle. This is exactly the same as Copy an angle with compass and straightedge.
1.  Make a point P that will be the apex of the new triangle.

2.  From P, draw a line. This will become one leg of the new triangle, so make it longer that FG.

  • This line can go off in any direction.
  • It does not have to be parallel to anything else.

3.  Place the compasses on point A, set to any convenient width.
4.  Draw an arc across both sides of the angle, creating the points J and K as shown.
5.  Without changing the compasses' width, place the compasses' point on P and draw a similar arc there, creating point M as shown.
6.  Set the compasses on K and adjust its width to point J.
7.  Without changing the compasses' width, move the compasses to M and draw an arc across the first one, creating point L where they cross.
8.  Draw a line from P through L and onwards further. This will become the second side (leg) of the triangle so make it longer than FG.
In the rest of the construction we set the lengths of the two legs and draw the base line.
9..   Place the compasses on point F and set its width to point G.
10.   Without changing the width, place the compasses on P and make an arc across both lines, creating points Q and R.
11.  Draw a line from Q to R.
DONE.  The triangle PQR is an isosceles triangle with each leg equal to the given FG in length, and the apex angle is equal in measure to the given angle CAB.
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Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions