Parts of a Triangle: Identifying and defining elements

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 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: $sides, main$.

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

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 $\text{Yes}$.

To solve whether the segment $DE$ is a side of one of the triangles, we must identify the sides of each triangle in the given diagram.

The first triangle is labeled $\triangle ABC$:

• Vertices are $A, B,$ and $C$.
• Sides by this configuration are $AB, BC,$ and $AC$.

The second triangle is labeled $\triangle DEF$:

• Vertices are $D, E,$ and $F$.
• Sides formed are $DE, EF,$ and $DF$.

Upon inspection, we see that $DE$ is listed as a side of $\triangle DEF$, confirming that it indeed is one side of this triangle.

Therefore, the conclusion is:

Yes, $DE$ is a side of one of the triangles.

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.

To determine if DF is a side in one of the triangles, we need to look at the vertices that define each triangle:

• Triangle 1: Vertices A, B, C
• Triangle 2: Vertices D, E, F

By identifying these vertices, we can list the triangle sides:

• For Triangle 1, the sides are: AB, BC, and CA.
• For Triangle 2, the sides are: DE, EF, and FD.

In Triangle 2, the segment DF is the same as FD, which confirms it is indeed a side of this triangle.

Therefore, the solution to the problem is yes, DF is a side of one of the triangles.

Let's solve the problem step-by-step.

• We first consider the two triangles given in the diagram. The vertices of the first triangle are labeled $A$, $B$, and $C$. The vertices of the second triangle are labeled $D$, $E$, and $F$.
• Identify the sides of the first triangle: Since the vertices are $A$, $B$, and $C$, the sides of the triangle are $AB$, $BC$, and $CA$.
• Identify the sides of the second triangle: With vertices $D$, $E$, and $F$, the sides are $DE$, $EF$, and $FD$.
• Now, we ascertain whether $BC$ is a side. Upon inspection, $BC$ is clearly the side connecting vertex $B$ and vertex $C$ in the first triangle.

Thus, we conclude that Yes, $BC$ is indeed a side of one of the triangles.

The solution to the problem is: Yes

The task is to determine if the segment $AD$ is a side of any of the given triangles. Based on the diagram, we have two distinct triangles:

• $\triangle ABC$: Formed by the points $A, B, C$.
• $\triangle DEF$: Formed by the points $D, E, F$.

For $\triangle ABC$, the sides are $AB, BC,$ and $CA$.

For $\triangle DEF$, the sides are $DE, EF,$ and $FD$.

In analyzing both triangles, we observe that:

• The side $AD$ is not listed as one of the sides of either triangle.

Thus, the conclusion is clear: AD is not a side of either triangle.

Therefore, the answer is No.

To solve this problem, we will inspect the two triangles in the diagram to determine if $AB$ can be identified as one of their sides.

1. We begin by examining the triangle on the left side, which is formed by points $A$, $B$, and $C$.
- Point $A$ is located at the top of the triangle, while point $B$ is at the bottom left.
- The diagram clearly shows a direct line connecting point $A$ to point $B$, therefore forming a side of this triangle.

2. There is another triangle on the right side of the diagram formed by points $D$, $E$, and $F$. However, since points $A$ and $B$ are not involved in this triangle, they cannot form a side of it.

Hence, it is evident that $AB$ is indeed a side of the left triangle, comprising points $A$, $B$, and $C$.

Therefore, the answer to the problem is Yes.

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.

The height of a triangle is defined as the perpendicular distance from a vertex to the line containing the opposite side (base). In this problem, we observe a vertical line segment drawn from a point on the base (horizontal line at the bottom of the triangle) to some level above the base. To determine if this line is a height, it must be perpendicular to the base and also reach to the opposite vertex of the triangle.

In the provided figure, the vertical line extends vertically from the base but does not connect to the opposite vertex of the triangle (at the top). Instead, it terminates at some intermediate point above the base. Since the line does not satisfy the full condition of being perpendicular and reaching an opposite vertex, it cannot be considered the height of this triangle.

Therefore, the given straight line is not the height of the triangle.

The correct and final answer is: No.

To determine if the straight line in the figure is the height of the triangle, we need to ensure it is a line that starts from a vertex of the triangle and is perpendicular to the opposite side, known as the base. In the context of geometry, this line is called an altitude.

According to the given figure, the straight line appears to stem from one vertex of the triangle and intersect the base at a right angle, as indicated by a small square or a perpendicular marker at their intersection.

Since the line in question meets the definition of an altitude (perpendicular from a vertex to the opposite side), it indeed represents the height of the triangle relative to that specific base.

Hence, the answer to the problem is Yes.

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 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 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 $BD$.