Triangle Angles Practice Problems - Sum Theorem Exercises

Since line segment DE does not correspond to a full side of any of the triangles present within the given geometry, we conclude that the statement “DE is a side in one of the triangles” is Not true.

To solve this problem, we'll follow these steps:

• Step 1: Examine the diagram presented.
• Step 2: Identify any familiar angle formations or configurations.
• Step 3: Use knowledge of angles to classify the type shown.
• Step 4: Determine the correct response from available options.

Observing the diagram:

The diagram includes two lines, one horizontal and the other vertical, extending fully. This horizontal extent along with the linear continuation suggests it forms an angle at the intersection with $180^\circ$. This indicates a straight angle.

We classify straight angles because an angle formed by two lines directly facing opposite directions is known to measure $180^\circ$. This diagrammatic representation aligns perfectly to confirm it calculates and visually shows a straight angle.

Thus, by recognizing these details within the diagram, we confirm the type of angle as Straight.

The problem involves classifying the angle represented visually, which looks like a semicircle with a central axis drawn. This indicates an angle that spans half a complete circle.

A complete circle measures $360^\circ$, so half of it, represented by a semicircle, measures half of $360^\circ$, which is $180^\circ$.

The four primary classifications for angles are:

• Acute: Less than $90^\circ$
• Right: Exactly $90^\circ$
• Obtuse: Greater than $90^\circ$ but less than $180^\circ$
• Straight: Exactly $180^\circ$

Since the angle measures exactly $180^\circ$, it is classified as a straight angle.

Therefore, the type of angle given is Straight.

The task is to determine whether the line shown in the diagram serves as the height of the triangle. For a line to be considered the height (or altitude) of a triangle, it needs to be a perpendicular segment from a vertex to the line that contains the opposite side, often referred to as the base.

Let's analyze the diagram:

• The triangle is described by its vertices, forming a shape, and one side is the base. There's a line drawn from one vertex directed toward the opposite side.
• To be the height, this line must be perpendicular to the side it meets (the base).
• Though the figure does not explicitly show perpendicularity with a right angle mark, the line appears as a straight, direct connection from the vertex to the base. This is typically indicative of it being a height.
• Assuming typical geometric conventions and the common depiction of heights in diagrams, the line shows properties consistent with being perpendicular to the opposite side, thereby functioning as the height.

Based on the analysis, the line is indeed the height of the triangle. Thus, the answer is Yes.

Therefore, the solution to the problem is Yes.

To determine if the straight line in the figure is the height of the triangle, we must verify the following:

• The line segment must extend from a vertex of the triangle and be perpendicular to the opposite side (or its extension).

In examining the figure provided, we notice that the triangle is formed by vertices at points $A, B,$ and $C$. Let's assume the base is the line segment $\overline{BC}$.

The line in question extends from a vertex $A$ and appears to intersect the base $BC$ at a right angle.

• Since it is extending from vertex to the opposite side and forming a right angle with it, this line meets the definition of an altitude.

Therefore, the line in the figure is indeed the height of the triangle. By confirming the perpendicular relationship, we determine that this geometric feature correctly describes an altitude.

Yes, the straight line in the figure is the height of the triangle.