Work out the size of angle x

Proving the congruent supplements theorem

An angle bisector ac divides a trapezoid abcd into two similar triangles ? abc and ? acd. find the perimeter of this trapezoid if the leg ab=9 cm and the leg cd=12 cm.

The figure shows triangle abc with medians a f, bd, and ce. segment a f is extended to h in such a way that segment gh is congruent to segment ag. triangle abc with medians ce, a f, and bd. median a f is extended to point h. a segment joins points b and h and another segment. which conclusion can be made based on the given conditions? segment gf is congruent to segment eg. segment gf is half the length of segment eb. segment gd is congruent to segment eg.segment gd is half the length of segment hc