Question

1. are the line segments congruent? (-1,5) (6,3) (2,3) (-1,1)

Explanation:

Step1: Calculate length of first - segment

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $(-1,1)$ and $(-1,5)$, $x_1=-1,y_1 = 1,x_2=-1,y_2 = 5$. Then $d_1=\sqrt{(-1+1)^2+(5 - 1)^2}=\sqrt{0 + 16}=4$.

Step2: Calculate length of second - segment

For points $(2,3)$ and $(6,3)$, $x_1 = 2,y_1=3,x_2 = 6,y_2=3$. Then $d_2=\sqrt{(6 - 2)^2+(3 - 3)^2}=\sqrt{16+0}=4$.

Step3: Check for congruence

The first segment is vertical and the second is horizontal. Although their lengths are equal, their orientations are different. In a more general sense, for non - parallel line segments, we also consider their slopes. The slope of the first segment (vertical) is undefined and the slope of the second segment (horizontal) is 0. Since the segments have different orientations, they are not congruent.

Answer:

No