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Write a proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Question

aihberkhan · Answer

Okay. 

Lets start by making an imaginary rectangle.

aihberkhan · Answer

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aihberkhan · Answer

Now just write the proof!

We started with the assumption that AC is not equal to BD and arrived at the contradiction that side AD is not equal to side BC.  But we know in a rectangle, AD = BC.  Therefore, our assumption AC is not equal to BD must be false.  Therefore, AC = BD.  The diagonals of a rectangle are congruent.

aihberkhan · Answer

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nicoleg7 · Answer

thanks and ill be sure too ;-)@AihberKhan

owlcoffee · Answer

A rectangle is a particular case of parallelograms, and I have proven in the tutorial I've written that the diagonals of any parallelogram intersect in their corresponding mid-points: http://assets.openstudy.com/updates/attachments/565bceb0e4b0b09ed5de4edc-owlcoffee-1448857315716-remake.pdf