Question

determine whether $overline{ab}$ and $overline{cd}$ are congruent. $overline{ab}$ and $overline{cd}$ are congruent not congruent plot $a(5, - 1), b(3, - 1), c(7,1),$ and $d(7, - 3)$

Explanation:

Step1: Use the distance - formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for line - segment $\overline{AB}$.

For points $A(5,-1)$ and $B(3,-1)$, $x_1 = 5,y_1=-1,x_2 = 3,y_2=-1$. Then $d_{AB}=\sqrt{(3 - 5)^2+(-1+1)^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2$.

Step2: Use the distance - formula for line - segment $\overline{CD}$.

For points $C(7,1)$ and $D(7,-3)$, $x_1 = 7,y_1 = 1,x_2 = 7,y_2=-3$. Then $d_{CD}=\sqrt{(7 - 7)^2+(-3 - 1)^2}=\sqrt{0^2+(-4)^2}=\sqrt{16}=4$.

Answer:

not congruent