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OpenSessame
 one year 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?
OpenSessame
 one year 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?

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OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0dw:1377490333537:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1I just made it a bit bigger. dw:1377490546842:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377490654352:dw

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0So I know the answer is, The rhombus is a square but i need help finding midpoints.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We can label all midpoints.

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Im guessingdw:1377490680684:dw

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0dw:1377490733250:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377490731812:dw

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Alright to do that you just add and divide right?

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Like the Xs and the Ys respectively?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Okay, easier then it sounds!

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we need to see what the quadrilateral made by connecting midpoints is.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377491112017:dw

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Then is you them into right triangles you find that it is a square?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377491168215:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Notice 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.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The next question is if the rhombus is also a square.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1All we need to do is to see if any two consecutive sides are perpendicular.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377491486110:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1One slope is 1. The other slope is 1. The slopes of two consecutive sides are negative reciprocals, so those two sides are perpendicular.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377491738087:dw Opposite angles of any parallelogram are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Also all angles added up are 360 degrees.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1377491805994:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.

OpenSessame
 one year ago
Best ResponseYou've already chosen the best response.0Yup:) hey! can you go back to the first question for a second?
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