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

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

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

OpenSessame
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1We can label all midpoints.

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

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

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

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

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

mathstudent55
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0Okay, easier then it sounds!

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

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

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

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

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

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

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

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

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

mathstudent55
 2 years 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
 2 years 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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