Parts of a Triangle: Identifying and defining elements

To solve the problem of determining whether DE is not a side in any of the triangles, we will methodically identify the triangles present in the diagram and examine their sides:

• Identify triangles in the diagram. The diagram presented forms a right-angled triangle ABC with additional lines forming smaller triangles within.
• Triangles formed: Triangle ABC (major triangle), Triangle ABD, Triangle BEC, and Triangle DBE.
• Let's examine the sides of these triangles:
• Triangle ABC has sides AB, BC, and CA.
• Triangle ABD has sides AB, BD, and DA.
• Triangle BEC has sides BE, EC, and CB.
• Triangle DBE has sides DB, BE, and ED.
• Notice that while point D is used, the segment DE is only part of line BE and isn't listed as a direct side of any triangle.

Therefore, the claim that DE is not a side in any of the triangles is indeed correct.

Hence, the answer is True.

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.

In the given diagram, we need to determine the height of triangle $\triangle ABC$. The height of a triangle is defined as the perpendicular segment from a vertex to the line containing the opposite side.

Upon examining the diagram:

• Point $A$ is at the top of the triangle.
• The side $BC$ is horizontal, lying at the base.
• Line segment $AD$ is drawn from point $A$ perpendicularly down to the base $BC$ at point $D$. This forms a right angle at $D$ with line $BC$.

Therefore, line segment $AD$ is the perpendicular or the height of triangle $\triangle ABC$.

Consequently, the height of triangle $\triangle ABC$ is represented by the segment $AD$.

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 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 $BD$.

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

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: $AD$.

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 $BD$.

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.

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.

To determine the type of angle, consider this interpretation:

• Step 1: Examine the angle formed by the depicted intersection of two lines in the diagram.
• Step 2: Compare the observed angle with known categories: an acute angle is less than $90^\circ$, an obtuse angle is greater than $90^\circ$ but less than $180^\circ$, and a straight angle is exactly $180^\circ$.
• Step 3: Visually, the angle appears sharp and much less than $90^\circ$, suggesting it is an acute angle.

Therefore, the type of angle in the diagram is Acute.

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.

In the given problem, we have a triangle depicted with a specific line drawn inside it. The question asks if this line represents the height of the triangle. To resolve this question, we need to discern whether the line is perpendicular to one of the sides of the triangle when extended, as only a line that is perpendicular from a vertex to its opposite side can be considered the height.

The line in question is shown intersecting one of the sides within the triangle but does not form a perpendicular angle with any side shown or the ground (as is required for it to be the height of the triangle). A proper height would typically intersect perpendicularly either at or along the extended line of the opposite side from a vertex.

Therefore, based on the visual clues provided and the typical geometric definition of a height (or altitude) in a triangle, this specific line does not fit the criteria for being a height.

Thus, we conclude that the line depicted is not the height of the triangle. The correct answer is No.

To determine whether the given line is the height of the triangle, we start by understanding what defines the height of a triangle. The height, or altitude, is a line segment drawn from a vertex perpendicular to the opposite side (the base), forming a right angle with that side.
We need to examine whether the specified line in the diagram is indeed perpendicular to the base of the triangle. If the line is not perpendicular, then it cannot be considered the height.

Upon examining the triangle in the SVG diagram, observe the following:

• The triangle, represented by vertices and sides, has a particular orientation.
• The line in question is drawn from one vertex to another interior point or appears in the interior of the triangle.
• Perpendicularity, if not explicitly shown by a right-angle marker, can also be evaluated by look or guided by other geometrical cues.
• In this case, the line does not appear to be perpendicular to any side explicitly. Usually, height serves as intersection at 90 degrees.

Since the line does not form a 90-degree angle with the triangle's base as determined upon inspection, it is not the height. Therefore, the correct conclusion is that the line shown is not the height of the triangle.

Therefore, the correct answer is: No.

To determine if the straight line is the height of the triangle, we'll analyze its role within the triangle:

• Step 1: Observe the triangle and the given line. The triangle seems to be made of three sides and a vertical line within it.
• Step 2: Recall that the height of a triangle, in geometry, is defined as a perpendicular dropped from a vertex to the opposite side.
• Step 3: Examine the positioning of the line: The vertical line starts at one vertex of the triangle and intersects the base, appearing to be perpendicular.
• Step 4: Verify perpendicularity: Given that the line is shown as a clear vertical (and a small perpendicular indicator suggests perpendicularity), we accept this line as the height.
• Step 5: Conclude with verification that the line is effectively meeting the definition of height for the triangle in the diagram.

Therefore, the vertical line in the figure is indeed the height of the triangle.

Yes

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.

The triangle's altitude is a line drawn from a vertex perpendicular to the opposite side. The vertical line in the diagram extends from the triangle's top vertex straight down to its base. By definition of altitude, this line is the height if it forms a right angle with the base.

To solve this problem, we'll verify that the line in question satisfies the altitude condition:

• Step 1: Identify the triangle's vertices and base. From the diagram, the base appears horizontal, and the vertex lies directly above it.
• Step 2: Check the nature of the line. The line is vertical when the base is horizontal, indicating perpendicularity.
• Conclusion: The vertical line forms right angles with the base, thus acting as the altitude or height.

Therefore, the straight line depicted is indeed the height of the triangle. The answer is Yes.

To solve this problem, we must determine whether the dashed line in the presented triangle fulfills the criteria of being a height. Let's verify each critical aspect:

• First, identify what a height (altitude) is: It is a line drawn from a vertex perpendicular to the opposite side.
• Next, observe the figure. We have a triangle with a dash line drawn from the top vertex to a side that seems to extend from one corner of the base to another point on the extended base.
• Since this line is not shown to be perpendicular to the base of the triangle (no right angle box), we cannot affirm that it fulfills our requirement.

As a result, the straight line does not meet the standard definition of a height for this triangle since it does not form the necessary 90-degree angle with the base. Therefore, as the line is not perpendicular to the opposite side, it is not the height.

Thus, the correct answer to the problem is No.

To determine if the given line in the triangle is the height, we need to check if it satisfies the conditions of a triangle's altitude.

• Step 1: Identify the base of the triangle. The problem suggests that the horizontal line, presumably at the bottom of the triangle, acts as the base.
• Step 2: The altitude must be drawn from the vertex opposite to the base and be perpendicular to this base. Thus, the potential altitude would start at the apex of the triangle.
• Step 3: The given figure features a straight line connecting two points on the interior of the triangle and is not perpendicular to the base.

Therefore, this line cannot be the height because it does not extend perpendicularly from the apex opposite the base to the base itself.

Thus, the correct answer is No.

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.