Triangle Angles Practice Problems - Sum Theorem Exercises

To determine the median of triangle ABC, we must identify a segment connecting a vertex of the triangle to the midpoint of the opposite side.

Examining the diagram, point F appears to be located on side AC. Given the configuration, point F divides side AC into two equal segments, which makes F the midpoint of AC.

Therefore, segment CF connects vertex C to the midpoint F of side AC. This characteristic aligns with the definition of a median in a triangle.

Hence, the median of triangle ABC is $CF$.

To solve this problem, we must identify which line segment in triangle ABC is the median.

First, review the definition: a median in a triangle connects a vertex to the midpoint of the opposite side. Now, in triangle ABC:

• Point A represents the vertex.
• Point E lies on line segment AB.
• Line segment EC needs to be checked to see if it connects vertex E to point C.

From the diagram, it appears that E is indeed the midpoint of side AB. Thus, line segment EC connects vertex C to this midpoint.

This fits the definition of a median, verifying that EC is the median line segment in triangle ABC.

Therefore, the solution to the problem is: $\text{EC}$.

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.

The task is to determine if the segment $AD$ is a side of any of the given triangles. Based on the diagram, we have two distinct triangles:

• $\triangle ABC$: Formed by the points $A, B, C$.
• $\triangle DEF$: Formed by the points $D, E, F$.

For $\triangle ABC$, the sides are $AB, BC,$ and $CA$.

For $\triangle DEF$, the sides are $DE, EF,$ and $FD$.

In analyzing both triangles, we observe that:

• The side $AD$ is not listed as one of the sides of either triangle.

Thus, the conclusion is clear: AD is not a side of either triangle.

Therefore, the answer is No.

To solve whether the segment $DE$ is a side of one of the triangles, we must identify the sides of each triangle in the given diagram.

The first triangle is labeled $\triangle ABC$:

• Vertices are $A, B,$ and $C$.
• Sides by this configuration are $AB, BC,$ and $AC$.

The second triangle is labeled $\triangle DEF$:

• Vertices are $D, E,$ and $F$.
• Sides formed are $DE, EF,$ and $DF$.

Upon inspection, we see that $DE$ is listed as a side of $\triangle DEF$, confirming that it indeed is one side of this triangle.

Therefore, the conclusion is:

Yes, $DE$ is a side of one of the triangles.