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 [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
The formula of a slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ L (-4 , -4) and M (-1 , -5)
∴ [tex]x_{1}[/tex] = -4 and [tex]x_{2}[/tex] = -1
∴ [tex]y_{1}[/tex] = -4 and [tex]y_{2}[/tex] = -5
- Use the formula of the distance to find LM
∵ [tex]LM=\sqrt{(-1--4)^{2}+(-5--4)^{2}}=\sqrt{9+1}[/tex]
∴ LM = [tex]\sqrt{10}[/tex]
∵ J (1 , 2) and K (-2 , 3)
∴ [tex]x_{1}[/tex] = 1 and [tex]x_{2}[/tex] = -2
∴ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 3
- Use the formula of the distance to find JK
∵ [tex]JK=\sqrt{(-2-1)^{2}+(3-2)^{2}}=\sqrt{9+1}[/tex]
∴ JK = [tex]\sqrt{10}[/tex]
- ML and JK have equal lengths
∴ LM ≅ JK
Use the formula of the slope to find the slopes of LM and JK
∵ [tex]m_{LM}=\frac{-5--4}{-1--4}=\frac{-5+4}{-1+4}[/tex]
∴ [tex]m_{LM}=-\frac{1}{3}[/tex]
∵ [tex]m_{JK}=\frac{3-2}{-2-1}=\frac{1}{-3}[/tex]
∴ [tex]m_{JK}=-\frac{1}{3}[/tex]
- 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
