The triangles shown here look like they might be congruent. Since we know the coordinates of all the vertices, we can compare side lengths using the Pythagorean Theorem—if we draw line segments (see the red dotted lines) that create two right triangles that have segments and as their respective hypotenuses. The length of segment is units because this segment is the hypotenuse of a right triangle with vertical side length of 3 units and horizontal side length of 2 units. The length of segment is units as well, because this segment is also the hypotenuse of a right triangle with leg lengths of 3 and 2 units.

The other sides of the triangles are congruent as well: The lengths of segments and are 1 unit each, and the lengths of segments and are each units, because they are both hypotenuses of right triangles with leg lengths 1 and 3 units (those lines are not shown, but could be drawn). So triangle is congruent to triangle by the Side-Side-Side Triangle Congruence Theorem.

Since triangle is congruent to triangle , there is a sequence of rigid motions that takes triangle to triangle . Here is one possible sequence: First, reflect triangle across the -axis. Then translate the image by the directed line segment from to .

Triangles ABC and A prime, B prime, C prime and DEF on a coordinate plane. A at 1 comma 1, B at 3 comma 4, C at 2 comma 4, D at -3 comma 1, E at -5 comma 4, F at -4 comma 4, A prime at -1 comma 1, B prime at -3 comma 4, C prime -2 comma 4.