Final answer:
Branson can prove that the diagonals of a rectangle are congruent by showing that the two triangles formed by drawing the diagonals share equal sides and angles, therefore making the triangles congruent, which in turn means their corresponding sides (the diagonals) are congruent.
Step-by-step explanation:
To prove that the diagonals in a rectangle are congruent, Branson can use the properties of a rectangle and congruent triangles. A rectangle is defined as a quadrilateral with four right angles. By drawing the diagonals of a rectangle, you are essentially creating two triangles which share a common side (the diagonal) and have two pairs of corresponding sides (the lengths of the rectangle) that are equal because opposite sides of a rectangle are equal in length. In addition, both triangles have a right angle. Since we know that side-side-angle (SSA) is enough to prove congruency in right-angled triangles, we can conclude that the two triangles are congruent. As corresponding parts of congruent triangles, the diagonals must therefore be congruent as well.