In order to prove the the diagonals the a rectangle room congruent, take into consideration the rectangle shown below. In this lesson, we will show you two various ways you have the right to do the same proof making use of the very same rectangle.

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The an initial way come prove the the diagonals of a rectangle space congruent is to show that triangle abc is congruent come triangle DCB

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

Since ABCD is a parallelogram, segment abdominal ≅ segment DC because opposite sides of a parallelogram space congruent.BC ≅ BC by the Reflexive home of Congruence. Furthermore, ∠ABC and also ∠DCB are ideal angles through the an interpretation of rectangle. ∠ABC ≅ ∠DCB due to the fact that all ideal angles space congruent. Summary segment abdominal muscle ≅ segment DC ∠ABC ≅ ∠DCB BC ≅ BC Therefore, by SAS, triangle abc ≅ triangle DCB. Due to the fact that triangle abc ≅ triangle DCB, segment AC ≅ segment BD

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

Here are some crucial things the you should be mindful of about the proof above. 

The reflexive property refers come a number the is constantly 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 space congruent, you can have additionally used triangle ABD and also triangle DCA. 

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

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

Since ABCD is a rectangle, that is additionally a parallelogram.

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