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I really need help on this question. Thanks in advance! A carpenter must ensure that a...

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it-sall-in-th... | eNoter

Posted April 30, 2013 at 7:47 PM via web

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I really need help on this question. Thanks in advance!

A carpenter must ensure that a large window frame is a rectangle. If the corners are labled E, F, G, and H the carpenter knows that EF=51 inches, FG=28 inches, GH=51 inches and EH=28 inches. The carpenter could measure the diagonals EG and FH and verify that they are the same length, but chooses another approach. After verifying that angle E is a right angle the carpenter insists that EFGH must be a true rectangle.

EFGH is a parallelogram since____________?

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oldnick | Valedictorian

Posted April 30, 2013 at 9:42 PM (Answer #1)

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It's enough to veirfy that a diagonal D:

`D=sqrt(EF^2+FG^2)`  for it'st true if only if  the angle are of 90°

Indeed, if the angle  `phi != 90°`  the diagonal, according Carnot's theorem, is:

`D=sqrt(EF^2+FG^2-2EF xx FG cos phi)`

This equation is equal  of that above is only if `cos phi=0`  that is `phi=90°`

 

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pramodpandey | College Teacher | Valedictorian

Posted May 1, 2013 at 6:21 AM (Answer #2)

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In ` DeltaHEF , angleE=90^o`

`Thus`

`HF^2=HE^2+EF^2```

`HF^2=51^2+28^2` , by Pythagoras Theorem.

Also

in `DeltaEHG`

`HE=28,HG=51=EF`

so

`HF^2=HE^2+HG^2=EG^2`

`HF=EG`

Thus triangle EHG congruent to triangle HEF by (SSS) crietrion.

this implies

`angleEHG=angleHEF=90`  ,But these are co-interior angles

Thus cointeror angles are supplementry ,thus

HG is parallel to EF.

Therefore EFGH are parallelogram ( opposite sides are parallel and equal 51 inch ).

 

HE=EH

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