What is the method to construct an isosceles triangle?

To construct an isosceles triangle, draw two equal-length sides from a common vertex and connect their endpoints.

To begin constructing an isosceles triangle, you need a ruler and a compass. First, decide on the length of the two equal sides. Let's call this length 'a'. Using your ruler, draw a straight line segment of length 'a'. This will be one of the equal sides of your isosceles triangle.

Next, place the compass point on one end of the line segment you just drew. Open the compass to the same length 'a' and draw an arc. Without changing the compass width, move the compass point to the other end of the line segment and draw another arc. The point where these two arcs intersect is the third vertex of your isosceles triangle.

Now, use your ruler to draw straight lines from this intersection point to each end of the original line segment. These lines are the other two sides of your isosceles triangle. You should now have a triangle with two sides of equal length 'a' and a base, which is the original line segment.

This method ensures that the triangle has two sides of equal length, making it isosceles. You can also use this technique to construct isosceles triangles with different side lengths by adjusting the compass width accordingly.