It is given that line EM is perpendicular to line AD, line BC is perpendicular to line AD, line AM is congruent to line DC, and line AB is congruent to DE.
Angle EMC and angle BCM are right angles because when two lines are perpendicular they form right angles. Angle EMC and angle BCM are congruent because if two angles are right angles then they are congruent. Line MC is congruent to line MC because a quantity is equal to itself. Line AC is congruent to line DM because if equal quantities are added to equal quantities, the sums are equal. Triangle EMD and triangle BCA are right triangles because a right triangle has one right angle. Triangle EMD is congruent to triangle BCA because two triangles are congruent if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle. Line BC is congruent to line EM because corresponding pats of congruent triangles are congruent.