Triangle Centroid Practice Problems & Median Intersection

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.

In geometry, the distance or length of a line segment between two points is the same, regardless of the direction in which it is measured. Consequently, the segments denoted by $BC$ and $CB$ refer to the same segment, both indicating the distance between points B and C.

Hence, the statement "BC = CB" is indeed True.

In order to determine if segment CB is a side of one of the triangles, let's start by identifying the triangles and their corresponding vertices from the given diagram:

• Triangle 1 has vertices labeled as A, B, C.
• Triangle 2 has vertices labeled as D, E, F.

Now, to decide if CB is a side, we need to check if a line segment exists between points C and B in any of these triangles.

Upon examining the points:

• Point C is present in triangle 1.
• Point B is also present in triangle 1.
• The line segment connecting B and C is visible, forming the base of triangle 1.

Therefore, segment CB is indeed a side of triangle ABC, confirming that the answer is Yes.

Thus, the solution to the problem is $\text{Yes}$.

In order to solve this problem, we need to understand the basic properties of an isosceles triangle.

An isosceles triangle has two sides that are equal in length, often referred to as the "legs" of the triangle. The angle formed between these two equal sides, which are sometimes referred to as the "sides", is called the "vertex angle" or sometimes more colloquially as the "main angle".

When considering the vocabulary of the given multiple-choice answers, choice 2: $sides, main$ accurately fills the blanks, as the angle formed between the two equal sides can indeed be referred to as the "main angle".

Therefore, the correct answer to the problem is: $sides, main$.