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Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?
 7 months ago
 7 months ago
Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?
 7 months ago
 7 months ago

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OpenSessameBest ResponseYou've already chosen the best response.0
dw:1377490333537:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
I just made it a bit bigger. dw:1377490546842:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377490654352:dw
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
So I know the answer is, The rhombus is a square but i need help finding midpoints.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
We can label all midpoints.
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Im guessingdw:1377490680684:dw
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
dw:1377490733250:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377490731812:dw
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Alright to do that you just add and divide right?
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Like the Xs and the Ys respectively?
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Okay, easier then it sounds!
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
Now we need to see what the quadrilateral made by connecting midpoints is.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377491112017:dw
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Then is you them into right triangles you find that it is a square?
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377491168215:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
Notice that every side of the new quadrilateral is the hypotenuse of a triangle with both legs measuring 2. Therefore, all sides of the quadrilateral are congruent, and the quadrilateral is a rhombus.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
The next question is if the rhombus is also a square.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
All we need to do is to see if any two consecutive sides are perpendicular.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377491486110:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
One slope is 1. The other slope is 1. The slopes of two consecutive sides are negative reciprocals, so those two sides are perpendicular.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377491738087:dw Opposite angles of any parallelogram are congruent.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
Also all angles added up are 360 degrees.
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
dw:1377491805994:dw
 7 months ago

mathstudent55Best ResponseYou've already chosen the best response.1
x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.
 7 months ago

OpenSessameBest ResponseYou've already chosen the best response.0
Yup:) hey! can you go back to the first question for a second?
 7 months ago
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