Question 933840
Let's look at your choices:
 
a. You measure and find opposite sides are the
same length.
The frame may look like this: {{{drawing(200,300,-22.5,22.5,-5,85,
line(-20,0,12,0),line(-12,80,20,80),
line(-20,0,-12,80),line(12,0,20,80),
green(line(-20,0,20,80)),green(line(12,0,-12,80))
)}}}
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: {{{drawing(200,300,-22.5,22.5,-5,85,
line(-20,0,20,0),line(-12,80,20,75),
line(-20,0,-12,80),line(20,0,20,75),
rectangle(20,0,18,2)
)}}} 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: {{{drawing(200,300,-22.5,22.5,-5,85,
line(-16,0,16,0),line(-16,80,16,80),
line(-16,0,-16,80),line(16,0,16,80),
green(line(-16,0,16,80)),green(line(16,0,-16,80)),
locate(-18,0,A),locate(-18,83,B),
locate(16.5,0,D),locate(16.5,83,C)
)}}} 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?
{{{drawing(200,300,-22.5,22.5,-5,85,
line(-22,0,22,0),line(-16,80,16,80),
line(-22,0,-16,80),line(22,0,16,80),
green(line(-22,0,16,80)),green(line(22,0,-16,80)),
locate(-22.5,0,A),locate(-18,83,B),
locate(21.5,0,D),locate(16.5,83,C)
)}}} 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.