Rectangles Have Congruent Diagonals

Here we must prove that a rectangle

• 1. Is a parallelogram

  2. Has congruent diagonals

The first one is easy. Because all angles are 90°, that means all corresponding angles are congruent, meaning that both pairs of lines are parallel.

Now lets prove that the diagonals are congruent. This is also pretty simple. First, notice that there are some triangles inside of this rectangle.

Now lets think about what we know. Because it is a rectangle, we know opposite sides are congruent, and thus AC ≅ BD. We know that ∠C ≅ ∠D because both are right angles. And both triangles share side CD. That gives us enough information for SAS to show those triangles are congruent. Now, with CPCTC, we know that AD ≅ BC, which means our diagonals are congruent and we're done.

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Prove that a rectangle

• 1. Is a parallelogram

  2. Has congruent diagonals