Chapter 5.2, Problem 18PPS

To determine

To identify: The BD.

Answer to Problem 18PPS

BD is an altitude, medium and perpendicular bisector of triangle ABC.

Explanation of Solution

Consider the below diagram.

  

From the above diagram, $\overline{B}\overline{D}\perp \overline{A}\overline{C}$ , thus $\overline{B}\overline{D}$ is an altitude of triangle ABC.

  $\overline{A}\overline{D}\cong \overline{C}\overline{D}$ , D is the midpoint of AC thus $\overline{B}\overline{D}$ is also a medium of triangle ABC.

  $\overline{B}\overline{D}\perp \overline{A}\overline{C}$ , D is the midpoint of AC, thus $\overline{B}\overline{D}$ is also a perpendicular bisector of triangle ABC.

Thus, BD is an altitude, medium and perpendicular bisector of triangle ABC.