anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1377490333537:dw|
mathstudent55
  • mathstudent55
I just made it a bit bigger. |dw:1377490546842:dw|
mathstudent55
  • mathstudent55
|dw:1377490654352:dw|

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More answers

anonymous
  • anonymous
So I know the answer is, The rhombus is a square but i need help finding midpoints.
mathstudent55
  • mathstudent55
We can label all midpoints.
anonymous
  • anonymous
Im guessing|dw:1377490680684:dw|
anonymous
  • anonymous
|dw:1377490733250:dw|
mathstudent55
  • mathstudent55
|dw:1377490731812:dw|
anonymous
  • anonymous
Alright to do that you just add and divide right?
anonymous
  • anonymous
Like the Xs and the Ys respectively?
mathstudent55
  • mathstudent55
Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.
anonymous
  • anonymous
Okay, easier then it sounds!
mathstudent55
  • mathstudent55
Now we need to see what the quadrilateral made by connecting midpoints is.
anonymous
  • anonymous
A rhombus!
mathstudent55
  • mathstudent55
|dw:1377491112017:dw|
anonymous
  • anonymous
Then is you them into right triangles you find that it is a square?
mathstudent55
  • mathstudent55
|dw:1377491168215:dw|
anonymous
  • anonymous
YEA:)
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
The next question is if the rhombus is also a square.
mathstudent55
  • mathstudent55
All we need to do is to see if any two consecutive sides are perpendicular.
anonymous
  • anonymous
Which they are!
mathstudent55
  • mathstudent55
|dw:1377491486110:dw|
mathstudent55
  • mathstudent55
One slope is 1. The other slope is -1. The slopes of two consecutive sides are negative reciprocals, so those two sides are perpendicular.
anonymous
  • anonymous
I get it:)
mathstudent55
  • mathstudent55
|dw:1377491738087:dw| Opposite angles of any parallelogram are congruent.
mathstudent55
  • mathstudent55
Also all angles added up are 360 degrees.
mathstudent55
  • mathstudent55
|dw:1377491805994:dw|
mathstudent55
  • mathstudent55
x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.
anonymous
  • anonymous
Yup:) hey! can you go back to the first question for a second?
mathstudent55
  • mathstudent55
ok

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