In order come prove the the diagonals the a rectangle room congruent, think about the rectangle shown below. In this lesson, us will present you two different ways you have the right to do the same proof utilizing the same rectangle.

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The an initial way to prove the the diagonals the a rectangle are congruent is to display that triangle abc is congruent come triangle DCB

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

Since ABCD is a parallelogram, segment abdominal muscle ≅ segment DC due to the fact that opposite political parties of a parallelogram are congruent.BC ≅ BC by the Reflexive building of Congruence. Furthermore, ∠ABC and also ∠DCB are appropriate angles through the meaning of rectangle. ∠ABC ≅ ∠DCB since all appropriate angles space congruent. Summary
segment abdominal muscle ≅ segment DC ∠ABC ≅ ∠DCB BC ≅ BC Therefore, through SAS, triangle alphabet ≅ triangle DCB. Since triangle alphabet ≅ triangle DCB, segment AC ≅ segment BD

Things the you have to keep in mind as soon as you prove that the diagonals the a rectangle are congruent.

Here space some necessary things that you must be conscious of around the proof above. 

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

The second way to prove the the diagonals that a rectangle space congruent is to display 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, that is also a parallelogram.

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Since ABCD is a parallelogram, segment ab ≅ segment DC because opposite political parties of a parallelogram room congruent.AD ≅ advertisement by the Reflexive property of Congruence. Furthermore, ∠BAD and also ∠CDA are right angles through the meaning of rectangle. ∠BAD ≅ ∠CDA since all right angles are congruent. Summary
segment ab ≅ segment DC ∠BAD ≅ ∠CDA advertisement ≅ ad Therefore, through SAS, triangle ABD ≅ triangle DCA. Since triangle ABD ≅ triangle DCB, segment AC ≅ segment BD
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