All terms in triangle calculation

A median in a triangle is a line segment connecting a vertex to the midpoint of the opposite side. Here, we need to find such a segment in triangle $\triangle ABC$.

Let's analyze the given conditions:

• $AD = \frac{1}{2}AB$: Point $D$ is the midpoint of $AB$.
• $BE = \frac{1}{2}EC$: Point $E$ is the midpoint of $EC$.

Given that $D$ is the midpoint of $AB$, if we consider the line segment $DC$, it starts from vertex $D$ and ends at $C$, passing through the midpoint of $AB$ (which is $D$), fulfilling the condition for a median.

Therefore, the line segment $DC$ is the median from vertex $A$ to side $BC$.

In summary, the correct answer is the segment $DC$.

A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. In triangle $\triangle ABC$, we need to identify such a median from the diagram provided.

Step 1: Observe the diagram to identify the midpoint of each side.

Step 2: It is given that point $E$ is located on side $AC$. If $E$ is the midpoint of $AC$, then any line from a vertex to point $E$ would be a median.

Step 3: Check line segment $BE$. This line runs from vertex $B$ to point $E$.

Step 4: Since $E$ is labeled as the midpoint of $AC$, line $BE$ is the median of $\triangle ABC$ drawn to side $AC$.

Therefore, the median of the triangle is $BE$ for $AC$.

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.

An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."

Therefore, the correct choice is Side, base.

Every triangle has 3 sides. First let's go over the triangle on the left side:

Its sides are: AB, BC, and CA.

This means that in this triangle, side EC does not exist.

Let's then look at the triangle on the right side:

Its sides are: ED, EF, and FD.

This means that in this triangle, side EC also does not exist.

Therefore, EC is not a side in either of the triangles.