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!

AB is a side in triangle ADB

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

In an isosceles triangle, the angle between ? and ? is the "base angle".

Step-by-Step Solution

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.

Answer

Side, base.

Exercise #2

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Every triangle has 3 sides. First let's go over the triangle on the left side:

Its sides are: AB, BC, and CA.

This means that in this triangle, side EC does not exist.

Let's then look at the triangle on the right side:

Its sides are: ED, EF, and FD.

This means that in this triangle, side EC also does not exist.

Therefore, EC is not a side in either of the triangles.

Answer

No

Exercise #3

According to figure BC=CB?

AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

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 BC and CB CB refer to the same segment, both indicating the distance between points B and C.

Hence, the statement "BC = CB" is indeed True.

Answer

True

Exercise #4

Look at the two triangles below.

Is CB a side of one of the triangles?

AAABBBCCCDDDEEEFFF

Step-by-Step Solution

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 Yes \text{Yes} .

Answer

Yes.

Exercise #5

Fill in the blanks:

In an isosceles triangle, the angle between two ___ is called the "___ angle".

Step-by-Step Solution

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,mainsides, 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,mainsides, main.

Answer

sides, main

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