Consider . If the midpoints of the sides are joined in order, the resulting quadrilateral must be a:
A)parallelogram
B)rectangle
C)kite
D)trapezoid

Question

Consider  . If the midpoints of the sides are joined in order, the resulting quadrilateral must be a:
A)parallelogram 
B)rectangle 
C)kite 
D)trapezoid

Quizplus · Accepted Answer

To determine the type of quadrilateral, we need to look at the properties of the midpoints of the sides. By joining the midpoints in order, we create the following segments:

_24__ │ __36_
  │     │
_9d__ │ __9b_
  │     │
ee84_ │ _11TB

Notice that opposite sides of the resulting quadrilateral are parallel. For example, segment _24_ is parallel to segment 9d__ because they are both midsegments of triangle 24d and triangle 9dB respectively. Similarly, segment __36 is parallel to segment ee84_ because they are both midsegments of triangle 36e and triangle e84T respectively.

Therefore, the resulting quadrilateral must be a parallelogram, and the answer is choice A).