All terms in triangle calculation

🏆Practice parts of a triangle

Terms used in triangle calculations

  • Line

A line is a general term for straight lines (hence its name) that extend from a specific point on the triangle.

  • Height

Height is a line that extends from a specific vertex and reaches perpendicularly to the opposite side, creating a right angle. The height is marked with the letter h (from the word height).

  • Median

The median is also a line extending from a specific vertex to the opposite side, but it reaches exactly the middle of the opposite side and divides it into two equal parts.

  • Angle Bisector

An angle bisector is a line that extends from a specific vertex and actually divides the vertex into two equal angles.

  • Perpendicular Bisector

A perpendicular bisector is a line that extends from the middle of a side perpendicular to it.

  • Midsegment

A midsegment is a line that connects the midpoints of two sides and is parallel to the third side, with its length being half of it.

  • Opposite Side

An opposite side is the side that is located opposite to a specific vertex and does not pass through it.

Diagram of a triangle ABC illustrating key geometric concepts: height (H) in green, median in blue, angle bisector in red, perpendicular bisector from CB in orange, midsegment in purple, and the side opposite to vertex A highlighted in orange. Labels are color-coded for clarity.

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Test yourself on parts of a triangle!

einstein

True or false:

DE not a side in any of the triangles.
AAABBBCCCDDDEEE

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Terms used in triangle calculations

Line

A ray is a general name for straight lines (hence its name) that extend from a specific point on the triangle.

Height

Height is a line that extends from a specific vertex and reaches perpendicularly to the opposite side, creating a right angle. Height is marked with the letter h (from the word height in English).

Median

The median is also a line that extends from a specific vertex to the opposite side, but it reaches exactly the middle of the opposite side and divides it into two equal parts.

Angle Bisector

An angle bisector is a line that extends from a specific vertex and divides the angle into two equal angles.

Perpendicular Bisector

A median perpendicular is a line that extends from the middle of a side perpendicular to it.

Midsegment

A midsegment is a line segment that connects the midpoints of two sides and is parallel to the third side, and its length is half of it.

Opposite Side

An opposite side is the side located across from a specific vertex and does not pass through it.

Diagram of a triangle ABC illustrating key geometric concepts: height (H) in green, median in blue, angle bisector in red, perpendicular bisector from CB in orange, midsegment in purple, and the side opposite to vertex A highlighted in orange. Labels are color-coded for clarity.

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Examples with solutions for Parts of a Triangle

Exercise #1

True or false:

DE not a side in any of the triangles.
AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

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.

Answer

True

Exercise #2

Is DE side in one of the triangles?
AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

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.

Answer

Not true

Exercise #3

True or false:

AB is a side of the triangle ABC.

AAABBBCCC

Video Solution

Step-by-Step Solution

To solve this problem, let's clarify the role of AB in the context of triangle ABC by analyzing its diagram:

  • Step 1: Identify the vertices of the triangle. According to the diagram, the vertices of the triangle are points labeled A, B, and C.
  • Step 2: Determine the sides of the triangle. In any triangle, the sides are the segments connecting pairs of distinct vertices.
  • Step 3: Identify AB as a line segment connecting vertex A and vertex B, labeled directly in the diagram.

Considering these steps, line segment AB connects vertex A with vertex B, and hence, forms one of the sides of the triangle ABC. Therefore, AB is indeed a side of triangle ABC as shown in the diagram.

The conclusion here is solidly supported by our observation of the given triangle. Thus, the statement that AB is a side of the triangle ABC is True.

Answer

True

Exercise #4

True or false:

AD is a side of triangle ABC.

AAABBBCCC

Video Solution

Step-by-Step Solution

To determine if line segment AD is a side of triangle ABC, we need to agree on the definition of a triangle's side. A triangle consists of three sides, each connecting pairs of its vertices. In triangle ABC, these sides are AB, BC, and CA. Each side is composed of a direct line segment connecting the listed vertices.

In the diagram provided, there is no indication of a point D connected to point A or any other vertex of triangle ABC. To claim AD as a side, D would need to be one of the vertices B or C, or a commonly recognized point forming part of the triangle’s defined structure. The provided figure and description do not support that AD exists within the given triangle framework, as no point D is defined within or connecting any existing vertices.

Therefore, according to the problem's context and based on the definition of the sides of a triangle, AD cannot be considered a side of triangle ABC. It follows that the statement "AD is a side of triangle ABC" should be deemed not true.

Answer

Not true

Exercise #5

True or false:

BC is a side of triangle ABC.

AAABBBCCC

Video Solution

Step-by-Step Solution

To solve this problem, we must determine whether BC is indeed a side of triangle ABC. A triangle consists of three vertices connected by three line segments that form its sides.

Firstly, observe the triangle labeled in the diagram with vertices A, B, and C. For triangle ABC, the sides are composed of the segments that connect these points.

  • The three line segments connecting the vertices are:
    • AB AB , connecting points A and B;
    • BC BC , connecting points B and C; and
    • CA CA , connecting points C and A.

Among these, BC is clearly listed as one of the segments connecting two vertices of the triangle. Therefore, BC is indeed a side of triangle ABC.

Hence, the statement is True.

Answer

True

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