Answer:
QRST is a rectangle.
Step-by-step explanation:
To decide whether this is a rectangle or not, we have the following options to choose from:
Prove that:
2 pairs of sides are parallel and one angle is 90°
2 pairs of opposite sides are equal and one angle is 90°
1 pair of sides is parallel and equal and one angle is 90°
All four angles are 90°
The diagonals are equal and bisect each other. (same midpoint)
I will go with option 1, because this only requires finding the slope of each of the 4 lines.
Note that:
points Q and R have the same
y
value
⇔
horizontal line
points S and T have the same
y
value
⇔
horizontal line
points Q and T have the same
x
value
⇔
vertical line
points R and S have the same
x
value
⇔
vertical line
Therefore QRST has to be a rectangle because horizontal and vertical lines meet at 90°.
The opposite sides are therefore parallel and equal and the angles are 90°
