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About Me
- egrasso10
- I like to play hockey. Food that is not good for me I still eat all the time, doritos and goldfish. I think it is cool when you watch Monday Night Football and the players give respect to their high school instead of college. WOW, that is the type of high school Norton should be, so amazing you want to mention how great it is whenever you can.
13 comments:
Q1. The quadrilateral iwth midpoints makes a perfect parraelogram (i butchered that word) with two sets of congruent lines and angles.
Q2.The diagonal of the quadrilateral is parallel to two sides of the parallelogram.The diagonal line that creates the two triangles in the quadrilateral is the line that is congruent to the other to sides of the parallelogram. The diagonal of the triangle does not seperate the parallelogram into two equal parts but does create two uneven triangles of the figure. The figure inside the quadrilateral is a parallelogram because it folllows all of the rules of that shape so it can be catagorized as a parallelogram. And thats it!! BOOM!! go to ur ROOM NOWWW
Q1- The midpoint shape is a parallelogram. The measurements support this because the two sides are parallel and the opposite parallel sides have the same lengths and slopes.
Q2- The shape made by the midpoints in clearly a parallelogram. This can be seen because the diagonal made through the original figure also cuts the parallelogram into two triangles. This happens when you have a parallelogram. If you take the original quadrilateral and cover a point with the point from the opposite side, the two pieces that cover each other are congruent.
1)It looks to me that the midpoint quadralateral is in fact a parraloogram.
2)I know that my statement in question 1 is correct because when the diagonal goes trough the parralelogam, it makes it symetrical. The triangles that the diagonal created made two egual triangles, which in turn makes the midpoint square a parralelogram.
Midpoint Quadrilaterals
Q1: The midpoint quadrilateral appears to be a parallelogram
The slopes and measurements of the opposite lines are congruent to each other
Q2: You know that your shape is a parallelogram because when your diagnol splits your shape in half it creates the two congruent triangles. Therefore when you take point a and drag it to point c you will find that your parallelogram is now one shape. This shows that your parallelogram is a symetrical shape and is split into two triangles.
The Golden Rectangle
Q1. The quadrilateral that appears in the middle of my figure is a rectangle. There are two sets of parallel lines that are opposite of each other. The opposite sides are the same lengths making it a rectangle. Line GH and Line EF are 1.01in, line HE and line FG are 1.83in.. The slopes are 0.5 and -1.1 for the opposite sides making a rectangle inside the quadrilateral.
Q2. The diagonal of the quadrilateral cuts it into two triangles. The diagonal also shares the same slope of two of the mid-segment lines; line GH and line EF have a slope of -1.1, and the diagonal has a slop of -1.1. Also, the length of the diagonal is twice as long as the line parallel to it. This makes the conjecture that the quadrilateral inside the original quadrilateral is in fact a rectangle because of the lengths and slopes of the lines mentioned before.
Q.1. The golden ratio is approximately 1.618.
-kady Ferguson
Geometry B,D
MIDPOINT QUAD
Q1. The midpoint quadrilateral is always a parallelogram. The opposites sides are parallel and congruent.
Q2. The lines have the same slope and distance because the two triangles are symmetrical. If you fold it over the diagonal, the two parts are the same. In my example, two of the opposite sides both have a slope of .8 and a length of 1.56. However you move the points, the opposite sides of the midpoint quadrilateral will always be the same length and have the same slope.
~TARYN
MIDPOINT QUAD
Q1. The midpoint quadrilateral is always a parallelogram. The opposites sides are parallel and congruent.
Q2. The lines have the same slope and distance because the two triangles are symmetrical. If you fold it over the diagonal, the two parts are the same. In my example, two of the opposite sides both have a slope of .8 and a length of 1.56. However you move the points, the opposite sides of the midpoint quadrilateral will always be the same length and have the same slope.
~TARYN
1. The midpoint quadrilateral appears to be a parallelogram. The measures of the slopes support this because two slopes are equal, and the other slopes are equal, proving two pairs of parallel sides.
2. The conjecture I made in question one is true because the midsegments of the triangles are parallel to the diagonal of the quadrilateral. If the midpoint quadrilateral was any shape but a parallelogram, this would not happen.
Meagan Elliott 1/16/09
Mr. Grasso Period BD
Geometers Sketchpad
Midpoint Quadrilaterals
Q1.) The kind of quadrilateral that the midpoint quadrilateral appears to be is a parallelogram. The measurements support these conjectures by the opposite sides are parallel. They are because they have the same slope. So lines HE and FG both have slopes of 0.2 and lines EF and HG have slopes of -1.4.
Q2.) The conjecture in number one is true. It is because the diagonal in the original quadrilateral is parallel to the two midsegments created in the two triangles. The diagonal created two triangles on either side. And the two midsegments are parallel to the diagonal. And that proves that the inside quadrilateral is a parallelogram. And if a parallelogram is bisected by a diagonal, the two triangles should be congruent and the midsegments should be parallel. So, if you pull one triangle over the other, they should show congruent measurements. So, yes it is a parallelogram. It is basically symmetry.
Q1. The quadrilateral is a parallelogram because the opposite sides of the midpoint quadrilateral are parallel and congruent.
Q2. The slope of the diagonal is the same as the slope of the two midsegments of the triangles created by the diagonal. No matter which way I draw the vertices, the slope of those three lines will always be equivalent. The two triangles created by the diagonal are also congruent. If I draw vertice D and place it on top of vertice B, all of the lines match up proving the triangle is congruent and also proving that this quadrilateral is a parallelogram. The midpoint quadrilateral is a parallelogram because the midsegments of the triangles and the diagonal have the same slope.
Midpoint Quadrilaterals:
1. The quadrilateral created appears to be parallelogram; the figure has parallel and congruent opposite sides.
2. According to the investigation, the slope of the diagonal line is the same as the slopes of the two opposite sides of the midsegment parallelogram. Even when the vertices of the original quadrilateral are dragged, the slope of the diagonal remains equivalent to that of the midsegment parallelogram. The diagonal line bisects the quadrilateral, creating two congruent triangles. One can prove that the two triangles are symmetrical by folding the original quadrilateral and matching up the vertices.
3. The Golden Ratio is 1.618.
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