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Rectangle HIJK has the points H(-4,1), I(1,1), J(1,-2)& K(-4,-2). Rectangle LMNO...

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connorcolin3 | Valedictorian

Posted December 19, 2011 at 6:05 AM via web

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Rectangle HIJK has the points H(-4,1), I(1,1), J(1,-2)& K(-4,-2). Rectangle LMNO has points L(-1,3), M(2,3), N(2,-3) & O (-1,-3). Are the rectangles congruent?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 19, 2011 at 7:36 AM (Answer #1)

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To find out if the rectangles are congruent we need to find the length of the sides of both rectangles.

We will find the length of the sides of the rectangle HIJK.

`==gt l HI l = sqrt((1+4)^2 + (1-1)^2)= sqrt(5^2)= 5. `

`==gt l IJ l = sqrt((-2-1)^2 + (1-1)^2)= sqrt(9)= 3`

`` Now we will find the length of the sides of the rectangle LMNO

`==gt l LM l = sqrt((3-3)^2 + (2-(-1))^2)= sqrt(9)= 3`

`==gt l MN l = sqrt((-3-3)^2 + (2-2)^2)= sqrt(36)= 6`

`` We notice that the sides of both rectangles are not equal.

Then rectangles HIJK and LMNO are NOT congruent.

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