SOLUTION: I've read this section of the chapter over and over again and I can't figure out exactly how I'm suppose to explain each of the situations?(Please Help!!!) While building the

Question 933840: I've read this section of the chapter over and over again and I can't figure out exactly how I'm suppose to explain each of the situations?(Please Help!!!)

While building the frame for a new door, you measure
to determine if the frame is a rectangle. For
each of the following situations, explain whether
you can conclude the frame is a rectangle.

a. You measure and find opposite sides are the
same length.

b. You measure and determine both diagonals are
the same length.

c. You measure one angle and determine it is a right angle.
Found 2 solutions by KMST, vleith:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let's look at your choices:

a. You measure and find opposite sides are the
same length.
The frame may look like this:
The opposite sides are the same length,
and that makes it a parallelogram,
but it is not a rectangle.
and the green diagonals are not the same length

c. You measure one angle and determine it is a right angle.
The frame may look like this: You have one right angle, just one,
but nothing matches; the angles and the sides, all have different measures.
That is not a rectangle.

b. You measure and determine both diagonals are
the same length.
The frame may look like this: This is a rectangle.
The book may say that if the diagonals are congruent, and bisect each other, it is a rectangle.
The book may say that if it is a parallelogram, and the diagonals are congruent, it is a rectangle.
However, what about this frame?
The diagonals are the same length, but is it a rectangle?
The diagonals are the same length, but they do not cross at their midpoints (they do not bisect each other).
In the US, that is called an isosceles trapezoid.
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
a. Imagine a diamond shape (rhombus). Are the opposite sides the same length? yes. Is it a rectangle? no
b. Now add in the measurement that the diagonals are equal. This makes the parallelogram a rectangle. So and and b together is a rectangle
c. Measuring a right angle only proves a and b were enough. In fact, a and c will also be enough

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