Think of the sides as transversals to two other sides of the quadrilateral.
See solution.
Practice makes perfect
We are asked to show that a quadrilateral with four right angles is a rectangle.
Let's look at two consecutive right angles at a time.
Since AB and DC are both perpendicular to AD, according to the Perpendicular Transversal Converse Theorem, these two sides of the quadrilateral are parallel.
AB≅DC
Let's focus on the other two parallel sides now.
Segments AD and BC are both perpendicular to AB, so they are also parallel.
AD≅BC
Since both pairs of opposite sides of quadrilateral ABCD are parallel, it is a parallelogram.
By definition, a parallelogram with four right angles is a rectangle, so ABCD is a rectangle.
Let's summarize the steps above in a paragraph proof as asked.
Completed Proof
2
&Given:&& ∠ A, ∠ B, ∠ C, and∠ D are right angles
&Prove:&& ABCD is a rectangle
Proof:
Since AB and DC are both perpendicular to AD, according to the Perpendicular Transversal Converse Theorem, AB∥DC.
Similarly, AD∥BC, since AD and BC are both perpendicular to AB.
Quadrilateral ABCD has two pairs of parallel sides, so by definition it is a parallelogram.
Quadrilateral ABCD is a parallelogram with four right angles, so by definition it is a rectangle
