Parts of a Triangle: Identifying and defining elements

The problem asks us to confirm if AB is a side of triangle ADB.

Triangle ADB is defined by its vertices, A, D, and B. A triangle is formed when three vertices are connected by three sides.

• Identify vertices: The vertices of the triangle are A, D, and B.
• Identify sides: The triangle's sides should be AB, BD, and DA.
• Observe: From the provided diagram, AB connects vertices A and B.

Therefore, based on the definition of a triangle and observing the connection between components, side AB indeed is a part of triangle ADB.

This confirms that the statement is True.

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.

To determine whether a plane angle can be found in a triangle, we need to understand what a plane angle is and compare it to the angles within a triangle.

• A plane angle is an angle formed by two lines lying in the same plane.
• In the context of geometry, angles found within a triangle are the interior angles, which are the angles between the sides of the triangle.
• Although the angles in a triangle are indeed contained within a plane (since a triangle itself is a planar figure), when referencing "plane angles" in geometry, we usually consider angles related to different geometric configurations beyond those specifically internal to defined planar shapes like a triangle.
• The term "plane angle" typically refers to the measurement of an angle in radians or degrees within a plane, but this doesn't specifically pertain to angles of a triangle.

Therefore, based on the context and usual geometric conventions, the concept of a "plane angle" is not typically used to describe the angles found within a triangle. Thus, a plane angle as defined generally in geometry is not found specifically within a triangle.

Therefore, the correct answer to the question is $\text{No}$.

To determine if a triangle can have a right angle, consider the following explanation:

• Definition of a Right Angle: An angle is classified as a right angle if it measures exactly $90^\circ$.
• Definition of a Right Triangle: A right triangle is a type of triangle that contains exactly one right angle.
• According to the definition, a right triangle specifically includes a right angle. This is a well-established classification of triangles in geometry.

Thus, a triangle can indeed have a right angle and is referred to as a right triangle.

Therefore, the solution to the problem is Yes.

The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.

Let us determine whether $DB$ is a side of triangle $ABC$. This verification depends greatly on understanding the arrangement and positioning of the points given within the triangle.

From the diagram, points $A$, $B$, and $C$ form a triangle because they create a closed figure with three lines connecting one another, typical of triangle sides. On examining point $D$ and the line $DB$, we notice that $D$ seems to be an internal point, potentially serving roles like that of a median or an angle bisector, but not forming an external side of triangle $ABC$.

Based on this understanding, line $DB$ fails to fulfil the requirement of connecting two of the vertices of the triangle directly. Hence, it's internal and is not counted as an external side of triangle $ABC$.

The conclusion based on the given options from the prompt: $DB$ is not a side of triangle $ABC$.

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 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 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 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.

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: $sides, main$.

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: $AD$.

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 $BD$.

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 if $EB$ is a side of either triangle, follow these steps:

• **Step 1:** Identify the vertices of the two triangles as shown in the diagram.
• **Step 2:** The first triangle has vertices $A$, $B$, and $C$. Hence, its sides are $AB$, $BC$, and $CA$.
• **Step 3:** The second triangle has vertices $D$, $E$, and $F$. Therefore, its sides are $DE$, $EF$, and $FD$.
• **Step 4:** Check if $EB$ is one of these sides.

On examining the sides listed for both triangles:

- For triangle $ABC$, we have sides $AB$, $BC$, and $CA$.

- For triangle $DEF$, we have sides $DE$, $EF$, and $FD$.

Clearly, $EB$ is not a side of either triangle.

Therefore, the solution to the problem is No, $EB$ is not a side of one of the triangles.

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.

To solve this problem, we need to understand what an isosceles triangle is and how its sides are labeled:

• In an isosceles triangle, there are two sides that have equal lengths. These are typically called the "legs" of the triangle.
• The third side, which is not necessarily of equal length to the other two sides, is known as the "base."

In terms of the problem, we want to determine the term used for the third side, which is the side that is not one of the two equal sides.

The correct term for the third side in an isosceles triangle is the "base." This is because the third side serves as a different function compared to the equal sides, which usually form the symmetrical parts of the triangle.

Among the given answer choices, choosing "Base" correctly identifies the third side of an isosceles triangle.

Therefore, the third side in an isosceles triangle is called the base.

Final Solution: Base

To solve this problem, we must analyze the provided geometric diagram carefully. The goal is to determine if line segment DE is a side of triangle BDC.

Let's examine the elements in the diagram:

• Triangle BDC is outlined with vertices B, D, and C.
• There is a line connecting points D and E, which does not coincide with the triangle's perimeter as sides are supposed to.
• A clear check shows us that sides BDC are formed by line segments BD, DC, and CB in the triangle.
• The line DE appears as an extension inside or outside of the triangle, making a clear indication that it is not part of the triangle itself.

Given the definition of a triangle's sides enclosed by its three vertices and the connectivity presented, it is apparent that DE is not recognized as one of the edges or sides that enclose triangle BDC.

Hence, the conclusion is: The statement "DE is a side in the triangle BDC" is Not true.