Triangle Centroid Practice Problems & Median Intersection

To solve this problem, we'll examine the image presented for the angle type:

• Step 1: Identify the angle based on the visual input provided in the graphical representation.
• Step 2: Classify it using the standard angle types: acute, obtuse, or straight based on their definitions.
• Step 3: Select the appropriate choice based on this classification.

Now, let's apply these steps:

Step 1: Analyzing the provided diagram, observe that there is an angle formed among the segments.

Step 2: The angle is depicted with a measure that appears greater than a right angle (greater than $90^\circ$). It is wider than an acute angle.

Step 3: Given the definition of an obtuse angle (greater than $90^\circ$ but less than $180^\circ$), the graphic clearly shows an obtuse angle.

Therefore, the solution to the problem is Obtuse.

To resolve this problem, let's focus on recognizing the elements of the triangle given in the diagram:

• Step 1: Identify that $\triangle ABC$ is a right-angled triangle on the horizontal line BC, with a perpendicular dropped from vertex $A$ (top of the triangle) to point $D$ on $BC$, creating two right angles $\angle ADB$ and $\angle ADC$.
• Step 2: The height corresponds to the perpendicular segment from the opposite vertex to the base.
• Step 3: Recognize segment $BD$ as described in the choices, fitting the perpendicular from A to BC in this context correctly.

Thus, the height of triangle $\triangle ABC$ is effectively identified as segment $BD$.

To determine the height of triangle $\triangle ABC$, we need to identify the line segment that extends from a vertex and meets the opposite side at a right angle.

Given the diagram of the triangle, we consider the base $AC$ and need to find the line segment from vertex $B$ to this base.

From the diagram, segment $BD$ is drawn from $B$ and intersects the line $AC$ (or its extension) perpendicularly. Therefore, it represents the height of the triangle $\triangle ABC$.

Thus, the height of $\triangle ABC$ is segment $BD$.

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.

To solve this problem, we need to identify the height of triangle ABC from the diagram. The height of a triangle is defined as the perpendicular line segment from a vertex to the opposite side, or to the line containing the opposite side.

In the given diagram:

• $A$ is the vertex from which the height is drawn.
• The base $BC$ is a horizontal line lying on the same level.
• $AD$ is the line segment originating from point $A$ and is perpendicular to $BC$.

The perpendicularity of $AD$ to $BC$ is illustrated by the right angle symbol at point $D$. This establishes $AD$ as the height of the triangle ABC.

Considering the options provided, the line segment that represents the height of the triangle ABC is indeed $AD$.

Therefore, the correct choice is: $AD$.