Question

Refer to $\Delta \mathbf{DEF}$ and name each of the following:

a. An altitude.

b. A median

c. The perpendicular bisector of a side of the triangle.

Short answer

a.Altitude of $\Delta DEF$is $\mathbf{DG}$.

b. Median of $\Delta DEF$is $\mathbf{FH}$.

c.Perpendicular bisector of $\Delta DEF$is$\mathbf{KJ}$.

Step-by-step solution

Step 1.  Write the definition of altitude.

An altitude is the perpendicular segment drawn from a vertex to the line containing the side opposite to that vertex.

Step 2.  Observe the given figure.

The given figure is:

From the given figure it can be noticed that $DG$ is the perpendicular segment drawn from the vertex $D$ to the line containing the side $EF$opposite to the vertex $D$.

Therefore, $DG$ is an altitude.

Step 3.  Description of step.

Therefore, altitude of $\Delta DEF$is $DG$.

Step 1.  Write the definition of median.

A median of a triangle is a segment from a vertex to the midpoint of the opposite side.

Step 2.  Observe the given figure.

The given figure is:

From the given figure it can be noticed that $DH=HE$ that implies $H$ is the midpoint of $DE$.

$DE$ is the opposite side to the vertex $F$, therefore $FH$ is a segment from vertex $F$ to the midpoint $H$ of the opposite side $DE$.

Therefore, $FH$ is the median of the triangle $\Delta DEF$.

Step 3.  Description of step.

Therefore, median of $\Delta DEF$is $FH$.

Step 1.  Write the definition of perpendicular bisector.

A perpendicular bisector of a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint.

Step 2.  Observe the given figure.

The given figure is:

From the given figure it can be noticed that $EJ=JF$ that implies $J$ is the midpoint of $EF$.

As, $\angle KJE=90°$, therefore by using the definition of perpendicular lines it can be said that $KJ\perp EF$.

Therefore, $KJ$ is the line that is perpendicular to the segment $EF$ at its midpoint.

Therefore, $KJ$ is the perpendicular bisector of the triangle $\Delta DEF$.

Step 3.  Description of step.

Therefore, perpendicular bisector of $\Delta DEF$is $KJ$.