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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 ?

In Exercises 1-3, plot the pointsAB and CD are congruent.1. A(-5, 5), B(-2,5)C(2, -4), D-example-1
User Sorashi
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SOLUTION

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.

User Tarkmeper
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