Answer:
The quadrilateral is a parallelogram because it has one pair of opposite sides that are both congruent and parallel ⇒ 2nd answer
Step-by-step explanation:
The formula of a distance between two points is
The formula of a slope of a line is
∵ L (-4 , -4) and M (-1 , -5)
∴ = -4 and
= -1
∴ = -4 and
= -5
- Use the formula of the distance to find LM
∵
∴ LM =
∵ J (1 , 2) and K (-2 , 3)
∴ = 1 and
= -2
∴ = 2 and
= 3
- Use the formula of the distance to find JK
∵
∴ JK =
- ML and JK have equal lengths
∴ LM ≅ JK
Use the formula of the slope to find the slopes of LM and JK
∵
∴
∵
∴
- ML and JK have same slopes
∴ LM // JK
∵ LM and JK are opposite sides in the quadrilateral
∵ LM ≅ JK
∵ ML // Jk
- Two opposite sides in the quadrilateral JKLM are congruent
and parallel
∴ JKLM is a parallelogram
The quadrilateral is a parallelogram because it has one pair of opposite sides that are both congruent and parallel