One way to reflect a triangle across a line of reflection is to reflect the vertices of the triangle, and then connect them.
Let the vertices be labelled A,B, and C with a line of reflection k.
To reflect point A across the line:
(1) Draw a circle centered at A that intersects k in two places; let the points of intersection be X and Y.
(2) Draw a circle centered at X with radius XY, and then a circle centered at Y with radius YX.
(3) Find the intersections of circle X and circle Y and connect them. This is the perpendicular bisector of `bar(XY)` and by construction will include A. (A is equidistant from the endpoints of the segment.)
(4) Label the point of intersection of the perpendicular bisector and k as point Z.
(5) Draw a circle centered at Z with radius ZA.
(6) The point of intersection of the diameter of circle Z and the perpendicular bisector is the reflection of point A, or A'.
Repeat this process for the other vertices and connect the image points with segments.