Proof

Among others, here is a proof I did recently that I like.
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Prove that the diagonals of a rectangle are congruent.

Given that points A, B, C, and D form a rectangle, according to the definition of a rectangle, Definition 4.26, it is a quadrilateral with all of its angles congruent. Theorem 4.97 also states that all of the congruent angles in a rectangle are right angles therefore implying that all consecutive sides are perpendicular. According to Theorem 3.25, diagonals can be formed with segments AC and BD thus forming triangles ABC and BAD.

As all of the consecutive sides are perpendicular, then Theorem 4.67 can be used to show that opposite sides of the rectangle are parallel meaning that quadrilateral ABCD is a parallelogram. Theorem 4.85 states that opposite sides of a parallelogram are congruent; therefore sides DA and BC are congruent and sides AB and CD are congruent. As all angles are congruent and right, then angles ABC and BAD are congruent. At this point, Theorem 4.18 can be used to show that triangles ABC and BAD are congruent. Using Theorem 4.20, the two diagonals can be concluded to be congruent. Therefore, it can be concluded that the diagonals of a rectangle are congruent.
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Definition 4.26: If all angles of a quadrilateral are congruent then the quadrilateral is a rectangle.

Theorem 4.97: The angles of a rectangle are all right angles.

Theorem 3.25: For any points A and B, both A and B lie on segment AB.

Theorem 4.67: If line l is perpendicular to line m and line m is perpendicular to line n then lines l and n are parallel.

Theorem 4.85: Opposite sides of a parallelogram are congruent.

Theorem 4.18: If points A, B, and C are non-collinear and points P, Q and R are non-collinear, then triangles ABC and PQR are congruent if and only if segments AB and PQ are congruent and segments BC and QR are congruent and angles ABC and PQR are congruent.

Theorem 4.20: If points A, B, and C are non-collinear and Points P, Q, and R are non-collinear, then triangles ABC and PQR are congruent if and only if segments AB and PQ are congruent and segments BC and QR are congruent and segments CA and RP are congruent.