Chapter 3.4, Problem 1PSA

a

To determine

Whether $\overline{AD}$ is median, altitude, neither or both.

Explanation of Solution

Given information : Here, we have given figure.

Proof: As, according to the figure, $\overline{AD}$ is dividing the base of triangle.

  $\Rightarrow$ $\overline{AD}$ is a median.

b

To determine

Whether $\overline{AD}$ is median, altitude, neither or both.

Explanation of Solution

Given information : Here, we have given figure.

Proof: As, according to the figure, $\overline{AD}$ is perpendicular to the base of triangle.

  $\Rightarrow$ $\overline{AD}$ is an altitude.

c

To determine

Whether $\overline{AD}$ is median, altitude, neither or both.

Explanation of Solution

Given information : Here, we have given figure.

Proof: As, according to the figure, $\overline{AD}$ is perpendicular to the base of triangle.

  $\Rightarrow$ $\overline{AD}$ is an altitude.

d

To determine

Whether $\overline{AD}$ is median, altitude, neither or both.

Explanation of Solution

Given information : Here, we have given figure.

Proof: As, according to the figure, $\overline{AD}$ is dividing the base of triangle as well as is perpendicular to the base.

  $\Rightarrow$ $\overline{AD}$ is a both median as well as an altitude.