How to Construct an Isosceles Triangle

1. 
   1
   Draw a line segment of the given length of the base.
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2. 
   2
   Set the width of your compass equal to the length of one of the equal sides.
3. 
   3
   Place the spike of the compass on one of the end points of the base (drawn in the first step), and draw an arc on either side of the base.
4. 
   4
   Without changing the width, place the spike of the compass on the other end point of the base. Draw another arc so as to cut the arc drawn in the previous step at some point.
5. 
   5
   Connect the point of intersection of the two arcs to each end point of the base.
   • The closed figure formed is the unique isosceles triangle adhering to the given dimensions.
     

1. 
   1
   Construct an angle of the given measure. Ensure that each of its arms are longer than the given side length.
2. 
   2
   Set the width of your compass equal to the length of one of the equal sides.
3. 
   3
   Place the spike of the compass on the vertex of the angle and strike off two arcs (one on each arm) to cut the arms at two different points.
4. 
   4
   Connect the two points of intersection of the arcs and the arms by a line segment - this line segment makes the base of the triangle.
   • The closed figure formed is the unique isosceles triangle adhering to the given dimensions.
     

The base angles of an isosceles triangle are the two angles which the base forms with the two equal sides. The two base angles are of the same measure.

1. 
   1
   Draw a line segment of the given length of the base.
2. 
   2
   Construct an angle of the given measure on one of the end points of the base, considering the base itself as one of the arms of the angle.
3. 
   3
   Construct another angle of the same measure on the other end point of the base, again considering the base itself as one of the arms of the angle.
   • The closed figure formed is the unique isosceles triangle adhering to the given dimensions.
     

1. 
   1
   Draw a line segment of the given length of the base.
2. 
   2
   Draw a line bisecting the base as described here. Thus, you also get to locate the mid-point of the base.
3. 
   3
   Set the width of the compass equal to the given length of the altitude.
4. 
   4
   Place the spike of the compass on the mid-point of the base and strike off an arc so as to cut the line bisecting the base at some point. You need to draw the arc only on one of the sides of the base.
5. 
   5
   Connect the point of intersection of the arc and the bisector line to each end point of the base.
   • The closed figure connecting the end points of the base to the point of intersection of the arc and the bisector line forms the unique isosceles triangle adhering to the given dimensions.
     
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