Question

two intersecting lines, $overline{ab}$ and $overline{de}$, are shown where $mangle dcb = 90^{circ}$. which of the following conclusions can be made using the given information? $overline{ab}$ is perpendicular to $overline{de}$ because they intersect at point $c$. $overline{ab}$ is not perpendicular to $overline{de}$ because point $c$ is not the mid - point of $overline{ab}$. $overline{ab}$ is perpendicular to $overline{de}$ because where they intersect, $angle bcd$ is a right angle. $overline{ab}$ is perpendicular to $overline{de}$ because they are not a horizontal and a vertical line intersecting.

Explanation:

Step1: Recall perpendicular - line definition

Two lines are perpendicular if the angle formed at their intersection is a right - angle (90°).

Step2: Analyze the given information

We are given that \(m\angle DCB = 90^{\circ}\), and \(\overline{AB}\) and \(\overline{DE}\) intersect at point \(C\). \(\angle DCB\) is the angle formed by the intersection of \(\overline{AB}\) and \(\overline{DE}\).

Answer:

\(\overline{AB}\) is perpendicular to \(\overline{DE}\) because where they intersect, \(\angle BCD\) is a right angle.