## 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?

1. OpenSessame

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2. mathstudent55

I just made it a bit bigger. |dw:1377490546842:dw|

3. mathstudent55

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4. OpenSessame

So I know the answer is, The rhombus is a square but i need help finding midpoints.

5. mathstudent55

We can label all midpoints.

6. OpenSessame

Im guessing|dw:1377490680684:dw|

7. OpenSessame

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8. mathstudent55

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9. OpenSessame

Alright to do that you just add and divide right?

10. OpenSessame

Like the Xs and the Ys respectively?

11. mathstudent55

Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.

12. OpenSessame

Okay, easier then it sounds!

13. mathstudent55

Now we need to see what the quadrilateral made by connecting midpoints is.

14. OpenSessame

A rhombus!

15. mathstudent55

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16. OpenSessame

Then is you them into right triangles you find that it is a square?

17. mathstudent55

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18. OpenSessame

YEA:)

19. 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.

20. mathstudent55

The next question is if the rhombus is also a square.

21. mathstudent55

All we need to do is to see if any two consecutive sides are perpendicular.

22. OpenSessame

Which they are!

23. mathstudent55

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24. 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.

25. OpenSessame

I get it:)

26. mathstudent55

|dw:1377491738087:dw| Opposite angles of any parallelogram are congruent.

27. mathstudent55

Also all angles added up are 360 degrees.

28. mathstudent55

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29. mathstudent55

x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.

30. OpenSessame

Yup:) hey! can you go back to the first question for a second?

31. mathstudent55

ok