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Checking a Building Foundation for Square
October 22-26, 1997
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One summer when I was in college my summer job was working on a crew that
was building a house. When I showed up for the first day of work, the
foundation was all poured, so we had a giant concrete rectangle. We
knew that the opposite sides of the rectangle were equal, but we didn't
know if the foundation was "square." By that I don't mean that all four
sides were equal, as in the polygon called a square, but that all of the
angles were 90 degrees, so that it was a real rectangle.
How did we figure out if all the angles were 90 degrees? We didn't have a protractor to measure the angles, but we did have a lot of string and a pretty long tape measure. How did we figure it out with just those tools? Remember to explain why your method works. (I learned a lot of neat geometry tricks that summer which I never learned in high school!) SolutionsThis is an interesting problem because while there are lots of ways to do it "theoretically," there is definitely a best way to do it "practically." "Theoretical" means that it will work mathematically, but might be a lot of work. "Practical" means you would actually do it on a construction site. I gave credit for both types of answers, but give that some thought when you are answering problems like this. 192 of you got it right - you turned in something that would actually tell us whether the angles were right angles or not. 28 folks got it wrong. There were three main ways of doing this. First is the diagonals method - measure the diagonals and see if they are equal. That's it! Tiffanie Lam of Sequoia Middle School provided a nice description and proof of this method, which is included below. If you used this method, you really should have included at least a little bit about why it works! The second is the Pythagorean theorem method. The best way to do this is by measuring the whole sides and the diagonals. This is illustrated by Andrew Fadden's submission. Andrew goes to Highland Park Senior High School. He points out that you don't have to measure all of the angles - since it is a parallelogram, certain angles have to be congruent anyway. A number of students did a miniature version of this method. They started at one corner and measured up one side 3 feet and up the other side 4 feet. Then they measured between their two points - if it's 5 feet, then it's a right angle. This is "theoretically" correct, meaning if you do the math it works out, but in real life it's not very practical. One, it's a lot of work, and second, what if you are off by a half an inch measuring your 5 feet? How far off could that angle be by the time you get 40 feet down that wall? This is an interesting problem, and might be one that we will use for the POW later in the year. Alison Miller, who is homeschooled, did the diagonal method and then mentioned using the Pythagorean Theorem. She noted that the diagonal method is a lot less work, and is better to use on a work site. That is what I mean by "practical" - you don't want to have to pull out a calculator just to check the foundation if there is an easier way. You can read Alison's solution below. A modification of the Pythagorean theorem method was used by Andrea Dexter-Rice of Nitschmann Middle School. She measured up the sides an equal amount, say 3 feet, on every single corner, and measured between her points at each corner. If all of the lengths were the same, then all the of the angles were the same. Since it is a parallelogram, the sum of the angles must be 360, so if they are all the same, they must all be 90. Good observation! A number of people came up with ways to show that all the angles were the same, but never said that that meant the angles had to be 90. This method suffers from the same possible problems as the 3-4-5 triangle method - small errors in measuring could lead to a lot of problems down the road. Christine Heyer of Odle Middle School came up with the diagonal method, but found it through the Pythagorean theorem - read her solution below to see how the two are related. A few students (mostly from Shaler Area High School) mentioned the "Housebuilder's Theorem," which states that if the diagonals of a parallelogram are congruent, then you've got a rectangle. Now that is a practical name for a theorem! Many students who used the diagonal method used string to get a length for the diagonals, and then measured the string. Too much work! Just use the string on one diagonal, then hold your spot on the string and move to the other diagonal. Is it the same? If so, you're all set. If not, you can fix it. We had a tape measure that was long enough to measure the whole diagonal, so we didn't actually use any string. You don't have to use both things that are given to you in the problem. Here's a request. If you don't know how to spell "Pythagorean," look it up! It is named after a person, after all, and you should learn how to spell both his name and the theorem named for him. A list of all the people who got this problem right follows the highlighted solutions below, and most of the solutions are also available.
From: Tiffanie Lam
Grade: 8
School: Sequoia Middle School, Pleasant Hill, California
First of all, we can use the tape to measure the two opposite sides.
If the opposite sides are equal for each side, then the foundation is
at least a parallelogram.
There are two ways you can check to see if it is a rectangle.
(1) If the tape or the strings are long enough, then just measure
the two diagonals. Diagonals with equal length means the
foundation is a rectangle.
PROOF:
A **************** B
* * * *
* * * *
* * * *
* ** *
* * * *
* * * *
D **************** C
Let's say we have AC = BD. Then because AD = BC
(paralellogram) and CD=CD, we have Triangle ADC congruent
to Triangle BCD. So, <ADC = <BCD. But, these angles are
supplement to each other. Therefore each angle must be
right angle or we have a rectagular foundation.
(2) If the strings or tape are not long enough, we can take a string and place
one end at the corner A and mark the two adjactent sides AD and
AB with the other end. Let say these two marks are W and X
respectively. Use the same string and place one end at D and
mark DA and DC at Y and Z, respectively, withe the other end of the
string. Now, use the tape measure WX and YZ. If WX=YZ, then the foundation
is a rectangle.
Proof:
AW=DY = AX=DZ and WX=YZ. So, Triangle WAX is congruent to Triangle
YDZ. So, <WAX = <YDZ. Since these two angle are supplement to each
other (parallelogram), <WAX = <YDZ = 90 degrees.
Therefore, the foundation is a rectangle.
From: Andrea Dexter-Rice
Grade: 8
School: Nitschmann Middle School, Bethlehem, Pennsylvania
My solution would be to measure a certain distance away from each corner, say
two feet. Then for each separate corner use a piecce of string to see how far
it is from the point two feet away on the right and the point two feet away on
the left. If the measurement was the same for all four corners, then all the
angles would have to be right angles because a parallelogram's angles add up to
360 degrees and 360 divided by four is 90 degrees.
From: Andrew Fadden
Grade: 9
School: Highland Park Senior High School, St. Paul, Minnesota
Subject: Oct 24 POW
Andrew Fadden, 9th grade, Geometry IB
Highland Park Senior High School, (612) 293-8940
www.stpaul.mn.us/hpsh/highland.html
From: Christie Heyer
Grade: 8
School: Odle Middle School, Bellevue, Washington
Subject: POW
Chrsitie Heyer
8th Grade
Odle Middle School
Art Mabbott
Dear Annie,
We know, according to the Pythagorean Theorum, that on a right
triangle the sum of leg A squared and leg B squared will be equal to the
hypotenuse squared. In your rectangle if you draw in the two diagonals you
get two right triangles, or they should be right triangles if the rectangle
is square. If you measure the distance of each hypotenuse they should be
equal because the legs of the triangles are equal. If A squared plus B
squared equals C squared on one right triangle and A and B are the same
length on the next right triangle, then both triangles' hypotenuses will be
C squared and equal to eachother. You can measure the hypotenuse by using a
piece of string. If the hypotenuses are equal then your rectangle is square.
From: Alison Miller
Grade: 6
School: homeschooled, Niskayuna, New York
Subject: Geometry POW October 22-26
Dear Annie,
In my picture, the foundation is the rectangle ABCD. My suggestion for
finding if all angles are 90 degrees is to measure the lengths of the two
diagonals, AD and BC, using the measuring tape and string. If their lengths
are equal, the foundation is a rectangle. Otherwise, the foundation is not.
The following students submitted correct solutions this week:Charlie Beigarten, Grade 10, Granada High School, Livermore, CaliforniaJason Chiu, Grade 9, Laramie Junior High School, Laramie, Wyoming Joe Chase, Grade 5, home Katie Anthony, Grade 9, Casady School, Oklahoma City, Oklahoma Julia Le, Grade 11, Minnechaug Regional High School, Wilbraham, Massachusetts Scott Mower, Grade 10, Cokeville High School, Cokeville, Wyoming Tiffanie Lam, Grade 8, Sequoia Middle School, Pleasant Hill, California Melinda Whiteman, Grade 10, Granada High School, Livermore, California Julie Hoover, Grade 10, Concordia Lutheran High School, Fort Wayne, Indiana Jayme Agbayani, Grade 9, Granada High School, Livermore, California Katie Madden, Grade 9, Mount Saint Joseph Academy, Flourtown, Pennsylvania Patrick Spephens, Grade 12, St. Louis High School, St. Louis, Missouri Will Marrs, Grade 9, Granada High School, Livermore, California Justin Onayemi, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois Sione Smythe, Grade , St. Joseph's Primary School, New Zealand Gordon Bockus Jr, Grade Freshman, Eastern Oklahoma State College, Wilburton, Oklahoma Laura Cowen and Sarah Molouki, Grade 10, Holton-Arms School, Bethesda, Maryland Christoph Mentz, Grade 13, Gymnasium, Germany Kenny Winters, Grade 7, South Preston Junior High School, Tunnelton, West Virginia Greg Schoppe, Grade 6, homeschooled, Lunenburg, Vermont Ryan Browning, Grade 9, Archmere Academy, Wilmington, Delaware Travis Talley, Grade 10, Franklin County High School, Rocky Mount, Virginia Jessica Sink and Katie Wright, Grade 9, Franklin County High School, Rocky Mount, Virginia Mary Ramsey, Grade 10, Franklin County High School, Rocky Mount, Virginia Brian Thompson, Grade 9, Franklin County High School, Rocky Mount, Virginia Ashley Tierney, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania Frannie Laks, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania Elizabeth Hammer, Grade 9, Our Lady of the Elms High School, Akron, Ohio Carl Yerger, Grade 9, Owen J. Roberts High School, Pottstown, Pennsylvania Jeremy Swaidner, Grade 9, Bowling Green High School, Bowling Green, Ohio Mark Beevers, Grade 8, South Fremantle Senior High School, Australia Zare Zarev, Grade 8, South Fremantle Senior High School, Australia Laurence Troy, Grade 8, South Fremantle Senior High School, Australia Joel Walker, Grade 8, South Fremantle Senior High School, Australia Michael Devenish, Grade 8, South Fremantle Sinior High School, Australia Hannah Margoles, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania Tracy Steed, Grade 12, Wilburton High School, Wilburton, Oklahoma Sean Kelly, Grade 7, Odle Middle School, Bellevue, Washington Honors Geometry Class, Grade 8, Dodge Middle School, Twinsburg, Ohio Dan Bruner, Grade , Carnegie Mellon University, Pittsburgh, Pennsylvania Adam Jamison, Grade 9, Franklin County High School, Rocky Mount, Virginia Kamila Sikora, Grade 9, Smoky Hill High School, Aurora, Colorado Paul Mersfelder, Grade 7, Far Hills Country Day School, Far Hills, New Jersey Candice Hebden, Grade 10, Penn Charter, Philadelphia, Pennsylvania Denny Chao, Grade 10, Germantown Academy, Fort Washington, Pennsylvania Keira Kushner, Grade 5, EGW Rosie Currier, Grade 8, Odle Middle School, Bellevue, Washington Justin Onayemi, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois Salma Ting, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois Ann Metiva, Grade 8, Center for the Arts and Sciences, Saginaw, Michigan Eve M., Grade 7, Far Hills Country Day School, Far Hills, New Jersey Jack M., Grade 7, Far Hills Country Day School, Far Hills, New Jersey Pooja Raval, Grade 7, Far Hills Country Day School, Far Hills, New Jersey Zach G., Grade 7, Far Hills Country Day School, Far Hills, New Jersey Rory C., Grade 7, Far Hills Country Day School, Far Hills, New Jersey Anna Wu, Grade 10, Monte Sant' Angelo Mercy College, Sydney, Australia Accelerated Geometry Class, Grade 10, Academy of the New Church, Bryn Athyn, Pennsylvania Laura Meyer, Grade 10, Concordia Lutheran High School, Tomball, Texas Joe Rodenbeck, Grade 9, Concordia Lutheran High School, Tomball, Texas Mackenzie Heims, Grade 9, Franklin County High School, Rocky Mount, Virginia Jamie Powell, Grade 9, Franklin County High School, Rocky Mount, Virginia Kaitlin Primavera, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania John Huff, Grade 9, Franklin County High School, Rocky Mount, Virginia Sara FitzSimmons and Jane Milton, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania Jim Hosch, Grade 9, Franklin County High School, Rocky Mount, Virginia Leanne Reidenbach, Grade 9, Franklin County High School, Rocky Mount, Virginia Tika Trotter, Grade 9, Franklin County High School, Rocky Mount, Virginia Tabitha Jones, Grade 9, Franklin County High School, Rocky Mount, Virginia Daniel Butler and Brian Brand, Grade 10 & 9, West Liberty High School Brian Chorney, Grade 8, Lincoln Middle School, Portland, Maine Alexandra Sowa, Grade 9, Archmere Academy, Wilmington, Delaware Ashley Monroe, Grade 9, Casady School, Oklahoma City, Oklahoma Ashley Johnson, Grade 9, Irving Middle School, Lincoln, Nebraska Corina Guishard, Grade , Oakcrest High School, Mays Landing, New Jersey Chester Chan, Grade 6, Odle Middle School, Bellevue, Washington Marko Garvin, Grade 12, Chapel Hill High School, Chapel Hill, North Carolina Delia Ryan, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania Mathew Steadman, Grade 8, Odle Middle School, Bellevue, Washington Madeline, Grade Year 11, Southland Girls' High School, New Zealand Megan Nowak, Grade 8, Odle Middle School, Bellevue, Washington Sangmin Lee, Grade 11, J.P. Taravella High School, Coral Springs, Florida Anthony Steele, Grade form 5, Westlake Boys' High School, New Zealand Andrew Wong, Grade 9, Farrington High School, Honolulu, Hawaii Sorin Ionescu, Grade 8, Ecole Secondaire Dorval, Montreal, Quebec, Canada Andrea Dexter-Rice, Grade 8, Nitschmann Middle School, Bethlehem, Pennsylvania Dennis S., Grade 5, Bishop Dunn Memorial School, Newburgh, New York Lin Qiu, Grade 10, Collegiate School, Richmond, Virginia Diane , Grade 9, Academy of Science & Technology, Conroe, Texas Sean McCarthy, Grade 9, Oakcrest High School, Mays Landing, New Jersey Patrick Tartar, Grade 8, Odle Middle School, Bellevue, Washington Jenny Kaplan, Grade 7, Castilleja Middle School, Palo Alto, California Jenny Lurie, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania Leslie Scott, Grade 9, Casady School, Oklahoma City, Oklahoma Patrick Feucht, Grade 9, West Point High School, West Point, Virginia Courtnie, Grade 10, Pullman High School, Pullman, Washington Mark Alvarez, Grade 10, Granada High School, Livermore, California Julia Fischer, Grade 10, Granada High School, Livermore, California Scott O'Donohue and Daniel Murnagh, Grade 8, South Fremantle High School, Fremantle, Australia Ylenia Adornato, Grade 6, Istituto Comprensivo, Novi di Modena, Italy Ita Kristiana and Sheridan Vella, Grade 8, South Fremantle Senior High School, Fremantle, Australia Mark Marshall, Grade 8, South Fremantle Senior High School, Fremantle, Australia Allison Chan, Grade 10, Mount Saint Joesph Academy, Flourtown, Pennsylvania John Martin, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Geometry 1B Class, Grade , Highland Park Senior High School, St. Paul, Minnesota Rachel Toaff, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania Dan Resnick and T.J. Wudarski, Grade 9 & 10, Germantown Academy, Fort Washington, Pennsylvania Clint Soose, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Christie Kubler and Jennie Doss, Grade 9, Franklin County High School, Rocky Mount, Virginia Tony Kambic, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Jordie Kvidera, Grade 7, Odle Middle School, Bellevue, Washington Amanda Gelik, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Melanie Hudak, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Lauren Moser, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Chris Casavale, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Nick LeDonne, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Emily Demich, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Stacie Lynch, Grade 10, Shaler Aea High School, Pittsburgh, Pennsylvania Susie Yardis, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Stacie Graham, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Alec Rzoski, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Cassi Van Steenburgh, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Dan Schwartzbauer, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Jason Gides, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Brandon Gilchrist, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Emily Buzicky, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Andrew Fadden, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Zimran Douglas, Grade 11, Wingate High School, Brooklyn, New York Laura Roos, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Joe Thomer, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Emily Schuler, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Emily Rozak, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Collin Tebo, Grade 7, Fair Hills Country Day School, New Jersey Chung Lee, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Clayton Dillaway, Grade 8, Odle Middle School, Bellevue, Washington Alicia Newton, Grade 10, Concordia Lutheran High School, Tomball, Texas Wendy Fishinger, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Jill Bisceglia, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Justin Dembowski, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Amy Tappe, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Kelly Flis, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Niki Weber, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Jen Erhart, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Robert Revay, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Gary Miller, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Sean McKean, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Jim Anglum, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Katie Schill, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Todd Sholos, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Mary Richardson, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Brian Fogle, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Kristina Meshanko, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Heather Beck, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Jill Filipovitz, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Lisa Didomenico, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Alexander Chen, Grade 8, Odle Middle School, Bellevue, Washington Paul Tarasi, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Matt Niederst, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Brian Vita, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Katie Beranek, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Lindsay Hastings, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Heather Nellis, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Lisa Isenhart, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Megan Bray, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania Christina Beran, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Heather Nalesnik, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Emily Fowler, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Lori Matesic, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Rachel Pytlik, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Paul Didomenico, Grade , Shaler Area High School, Pittsburgh, Pennsylvania Alison Falkenhagen, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Eric Collins, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Rashida Fisher, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Kelsey Long, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Krystal Schuman, Grade 9, Highland Park Senior High School, St. Paul, Minnesota Allen Hsu, Grade , Nitschmann Middle School, Bethlehem, Pennsylvania Mike Sands, Grade , Nitschmann Middle School, Bethlethem, Pennsylvania Tim Peterson, Grade 7, homeschooled, Rochester, New York Christie Heyer, Grade 8, Odle Middle School, Bellevue, Washington Zach Kilgore, Grade 8, York Middle School, York, Maine Thomas Kuo, Grade 10, Burroughs High School, Ridgecrest, California Anna Warszawa, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Xiaochang Li, Grade 8, Odle Middle School, Bellevue, Washington Alison Miller, Grade 6, homeschooled, Niskayuna, New York Matthew Harrison, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Zach Dillon, Grade 7, Odle Middle School, Bellevue, Washington Andrew Cooledge, Grade 7, Odle Middle School, Bellevue, Washington Jennifer Liang, Grade 8, Odle Middle School, Bellevue, Washington Lev Navarre, Grade 6, Odle Middle School, Bellevue, Washington Eric Dubas, Grade 9, Germantown Academy, Fort Washington, Pennsylvania Josh Kinney, Grade 7, Chillicothe Junior High School, Chillicothe, Illinois Katie Clark, Grade 9, Shaler Area High School, Pittsburgh, Pennsylvania Cory Campbell, Grade , Shaler Area High School, Pittsburgh, Pennsylvania |
I used the converse of the Pythagreon Theorem to figure out this Problem of the
Week. To be a rectangle, AC = BD and AB = CD, and all four angles have to be
right angles.
The converse of the Pythagreon Theorem guarantees a right triangle.
If AC^2 + CD^2 = AD^2, then angle C is a right angle. The same thing is true
with AB^2 + BD^2 = AD^2. If this is true then angle B is also a right angle. If
you find out that both angle C and angle B are right angles, then you know that
it is a rectangle because if a parallelogram has 2 right angles then all four
angles have to be right angles.
So to figure out if your slab of concrete is a rectangle all you have to do is
measure two of the sides and the diagonal, and plug the numbers into a^2 + b^2 =
c^2.
I am going to show that if the lengths of the diagonals are equal, that is,
AD=BC, then the foundation is a rectangle. We have been given that opposite
sides are equal, that is AB=CD, and AC=BD. Now take the two triangles ACD and
BCD. They share the side CD, and we know that AC and BD are equal, and that
AD and BC are also equal. Therefore by SSS, the triangles ACD and BCD are
congruent. That means that angle ACD= angle BCD. By the same reasoning, all 4
angles of our foundation are equal, and so they are 90 degree angles (because
the sum of the angles of a quadrilateral is 360 degrees.)
If the lengths of the diagonals are not equal, the foundation can't be a
rectangle because rectangles have equal diagonals, by the Pythagorean Theorem.
You can also use the converse of the Pythagorean Theorem to find out if the
foundation is a rectangle but it's harder and you don't have a calculator!
Alison Miller, Grade 6
Homeschooled, Niskayuna, NY
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