Question

As part of constructing an isosceles triangle, Gail drew a line segment and plotted one vertex of the triangle on the line segment. With this vertex as the center, Gail drew an arc to create a 180 degree angle. How can Gail ensure that the two other points she plots will be the remaining two vertices of an isosceles triangle?

Answer 1

See basically, this should be your diagram


In isosceles triangle, length of any two sides are equal.
Let O be the vertex and consider an arc of radius 5 cm drawn as shown above. Now consider a line parallel to AB passing through the arc. The two points where it meets the arc are the remaining two vertices of the isosceles triangle