In order to prove the the diagonals of a rectangle space congruent, take into consideration the rectangle shown below. In this lesson, us will display you two various ways you can do the same proof utilizing the same rectangle.

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The very first way come prove the the diagonals of a rectangle space congruent is to display that triangle alphabet is congruent to triangle DCB

Here is what is given: Rectangle ABCDHere is what you must prove: segment AC ≅ segment BD
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Since ABCD is a rectangle, that is likewise a parallelogram.

Since ABCD is a parallelogram, segment abdominal ≅ segment DC due to the fact that opposite sides of a parallelogram space congruent.BC ≅ BC by the Reflexive property of Congruence. Furthermore, ∠ABC and ∠DCB are ideal angles through the an interpretation of rectangle. ∠ABC ≅ ∠DCB since all right angles space congruent. Summary
segment ab ≅ segment DC ∠ABC ≅ ∠DCB BC ≅ BC Therefore, by SAS, triangle alphabet ≅ triangle DCB. Because triangle alphabet ≅ triangle DCB, segment AC ≅ segment BD

Things the you should keep in mind as soon as you prove that the diagonals that a rectangle room congruent.

Here room some crucial things the you should be aware of around the proof above. 

The reflexive residential or commercial property refers to a number that is always equal come itself. Because that example, x = x or -6 = -6 are instances of the reflex property. In order to prove that the diagonals of a rectangle are congruent, you could have likewise used triangle ABD and triangle DCA. 

The second way to prove the the diagonals the a rectangle room congruent is to present that triangle ABD is congruent come triangle DCA

Here is what is given
: Rectangle ABCDHere is what you have to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is likewise a parallelogram.

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Since ABCD is a parallelogram, segment abdominal ≅ segment DC because opposite sides of a parallelogram space congruent.AD ≅ ad by the Reflexive residential property of Congruence. Furthermore, ∠BAD and ∠CDA are right angles by the an interpretation of rectangle. ∠BAD ≅ ∠CDA due to the fact that all best angles space congruent. Summary
segment abdominal ≅ segment DC ∠BAD ≅ ∠CDA advertisement ≅ ad Therefore, by SAS, triangle ABD ≅ triangle DCA. Due to the fact that triangle ABD ≅ triangle DCB, segment AC ≅ segment BD
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