Question

Write either in a 2 column or flow chart proof please​

Answer 1

Yes, the midpoint of a rectangle is its center. Imagine a diagonal line cutting through the rectangle. The midpoint of this line is also the center of the rectangle, where all sides are equidistant.

Yes, the statement in the image is correct. The midpoint of a rectangle is indeed the center of the rectangle. This can be proven using the properties of parallel lines and transversals.

In the image,
`$\overline{AC}$` is a transversal that intersects two parallel lines,
`$\overline{AB}$` and
`$\overline{DC}$`. Since
`$\overline{AB}||`
`\overline{DC}$`, we know that
`$\angle AEB \cong \angle CED$`and
`$\angle BEC \cong \angle ACB$`(corresponding angles). Additionally, we are given that
`$\overline{BE} \cong \overline{DE}$` (since E is the midpoint of
`$\overline{BD}$`).

Using the Angle-Angle-Side (AAS) congruence rule, we can then conclude that
`$\triangle AEB \cong \triangle CED$`. This means that the two triangles have the same corresponding side lengths and angles. Therefore,
`$\overline{AC}$` must bisect
`$\overline{BD}$` at point E, making E the center of the rectangle.