Given: WXYZ is a parallelogram. WY and XZ bisect each other and WY is perpendicular to XZ. Conclusion: WXYZ is a rectangle. Determine if the conclusion is valid

Question

This was super difficult for me and no matter how hard I tried, I couldn't figure it out! If someone could help me that would be awesome! Thank you!

Answer 1

It is difficult to draw on this platform.  Still:

 

Draw a horizontal line... label one end x, the other end y

Draw a vertical line that intersects at the middle of line segment xy...

         with half of the vertical line above line xy and half below...

         Label the top point as w and the bottom point at z

 

                     w

                      |b

            a        |          a

    x  -----------|------------y

                      |

                      | b

                      z

 

Connect the 4 outside points x→w, w→y, y→z, z→x

Basically you have a diamond shape...

 

Letting o be the middle point where the lines intersect..

xo = oy ....   Call that distance "a"

zo = wo ....  Call that distance "b"

 

You are looking at 4 right triangles.  xw, wy, yz, and zx are

each a hypotenuse...

From Pythagorean theorem each is length √(a²+b²)

 

You have a parallelogram with 4 equal side lengths...

Basically it's a square set up on one point...

That is indeed a rectangle.