Question

In Exercises 1-3, plot the pointsAB and CD are congruent.1. A(-5, 5), B(-2,5)C(2, -4), D(-1, -4)Is Line AB and Line CD congruent ?

Answer 1

To check if line AB and CD are congruent, let's check if their length or distances are equal.

To do this, we will use the distance formula

distance between A(-5, 5), B(-2,5) is

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1))^2 \\ d=√((-2-(-5)^2+(5-5)^2) \\ d=√((-2+5)^2+0) \\ d=√(3^2) \\ d=√(9) \\ d=3\text{ units } \end{gathered}`

The distance or length CD becomes

distance between C(2, -4), D(-1, -4), we have

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1))^2 \\ d=√((-1-2)^2+(-4-(-4)^2) \\ d=√((-3)^2+(-4+4)^2) \\ d=√(9+0^2) \\ d=√(9) \\ d=3\text{ units } \end{gathered}`

Since AB and CD = 3 units, hence AB and CD are congruent.