The sides or edges of a triangle

The sides of a triangle

Every triangle has three sides. That also works the other way around - if we see a shape with tree sides, it's a triangle.

types of triangles based on the sides:

The sides allow us to classify the different types of triangles according to their size:

Equilateral: All sides are equal, leading to equal angles.
Isosceles: Two sides are equal, with base angles also equal.
Scalene: All sides are different lengths, with all angles unique.

Perimeter of a Triangle

Like every polygon, the sides of a triangle form its perimeter. To find the perimeter of a triangle, simply add the lengths of all three sides.

Relation between the sides and the angles in a triangle

In a triangle, there’s a direct relationship between the length of a side and the size of the angle across from it:
The Longer Side will always be in the opposite side of the larger Angle, and the shorter side will always be in the opposite side of the smaller Angle.

Can every three lines form a triangle?

In any triangle, the sum of the two shorter sides must always be greater than the length of the third side. This rule, known as the Triangle Inequality Theorem, ensures that the sides can actually form a closed triangle. For example, if the two shorter sides are not greater than the third, the sides would lie flat rather than forming a triangle. This principle is crucial in determining whether a set of side lengths can create a valid triangle.

Detailed explanation

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Test yourself on parts of a triangle!

True or false:

DE not a side in any of the triangles.

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Perimeter of the triangle

Recall that the perimeter of a plane figure is its edge, so in a triangle the perimeter is the sum of its three sides (edges).

A condition satisfied by the measures of the sides (or edges) of a triangle.

In any triangle the sum of the length of any two of its sides must be greater than the length of the third side.

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Test your knowledge

Question 1

Is DE side in one of the triangles?

Question 2

True or false:

AB is a side of the triangle ABC.

Question 3

True or false:

AD is a side of triangle ABC.

Examples of the subject

Example 1

Given a triangle with sides $4~cm$ , $3~cm$ and $5~cm$ . Calculate the perimeter.

Solution

We know that the perimeter of a triangle is the sum of its three sides, therefore,

$P=4\operatorname{cm}+3\operatorname{cm}+5\operatorname{cm}$

Answer:

$P=12\operatorname{cm}$

Example 2

Tell if it is possible to construct a triangle in which its sides measure $3~cm$ , $4~cm$ and $8~cm$ .

Solution

Recall that in order to construct a triangle, the sum of any two sides must be greater than the third side.

If we add the sides with measures $3~cm$ and $4~cm$ , we get as a result $7~cm$ , which is less than the third side.

Answer:

Therefore, it is not possible to construct a triangle with the given measures.

Do you know what the answer is?

Question 1

True or false:

BC is a side of triangle ABC.

Question 2

ABC is an isosceles triangle.

AD is the median.

What is the size of angle $∢\text{ADC}$ ?

Question 3

AD is the median in triangle ABC.

BD = 4

Find the length of DC.

Example 3

If an equilateral triangle has perimeter $P=21\operatorname{cm}$ . How long is each side?

Solution

Since the triangle is equilateral we know that its sides are equal, so we just divide the perimeter by three to get the measure of each side. lado.

$P=3x$

$21\operatorname{cm}=3x$

$x=21\operatorname{cm}:3$

Answer:

$x=7\operatorname{cm}$

Example 4

Tell if it is possible to construct a triangle in which its sides measure $5~cm$ , $7~cm$ and $10~cm$ .

Solution

We add the lengths of any two sides (edges) and compare with the length of the remaining side.

$5~cm + 7~cm= 12~cm$ which is greater than the remaining side that measures $10~cm$
$7~cm + 10~cm = 17~cm$ The length of the remaining side, which is greater than the remaining side measuring $5~cm$ , is greater than the remaining side measuring $5~cm$ .
$10~cm + 5~cm = 15~cm$ , which is greater than the remaining side measuring $7~cm$ .

Answer:

So if it is possible to construct a triangle of measures $5~cm$ , $7~cm$ and $10~cm$ on each side.

Check your understanding

Question 1

Given the following triangle:

Write down the height of the triangle ABC.

Question 2

Given the following triangle:

Write down the height of the triangle ABC.

Question 3

Given the following triangle:

Write down the height of the triangle ABC.

Questions on the subject

How many sides does a triangle have?

A triangle has three sides.

How many edges does a triangle have?

A triangle has three edges.

What are the edges of a triangle?

The edges of a triangle, commonly called the sides of a triangle, are the straight lines that bound the faces of the triangle.

What are the edges of a figure?

In a plane figure, the edges or sides are the line segments that join two vertices, and form the outline or perimeter of the figure.

Exercises on the sides or edges of a triangle

Exercise 1

Query

$DE$ Does that side not exist as part of any of the triangles?

Consignment DE This side does not exist as part of any of the triangles.

Solution

A side in a triangle is a line that passes between one of the 3 points that are the angles of the triangle.

In this case the line $DE$ does not pass between the extreme angles of any of the triangles but goes out through a point $D$ which is in fact an angle in a triangle $\triangle DBC$ but $DE$ ends at the point $E$ which is not an angle in any of the triangles in the figure.

Answer

True

Do you think you will be able to solve it?

Question 1

Which of the following is the height in triangle ABC?

Question 2

Given the following triangle:

Write down the height of the triangle ABC.

Question 3

Given the following triangle:

Write down the height of the triangle ABC.

Exercise 2

Question:

Do the triangles in the drawing overlap?

Solution

We can observe that according to the theorem of superposition: side, side, angle.

We can observe that there are 2 sides equal in length and an angle equal in size.

Answer

Yes

Exercise 3

Question

What type of triangle is drawn here?

Solution

It can be seen that in this triangle each of its three angles is of different size so it can be said that it is a scalene triangle.

Answer

Scalene triangle

Test your knowledge

Question 1

Determine the type of angle given.

Question 2

Determine the type of angle given.

Question 3

True or false:

DE not a side in any of the triangles.

Exercise 4

Consigna

Given the following triangle:

The perimeter of the triangle is $17$

How much is $X$ ?

Solution

To solve the task we replace all the data we have in the equation to calculate the perimeter of the triangle:

$2X+3X+3.5X=17$

Let's remember... The perimeter of the triangle is equal to the sum of its 3 sides.

If we calculate the equation we find that:

$8.5X=17$

We divide the equation by $8.5$ to find the value of. $X$

$\frac{8.5X}{8.5}=X=\frac{17}{8.5}=2$

Answer

$2$

Exercise 5

Request

Given the equilateral triangle

The perimeter of the triangle is $33\operatorname{cm}$ , what is the value of $X$ ?

Solution

One of the characteristics of an equilateral triangle is obviously that each of its sides are equal, i.e. if one side is worth $11$ all its sides will be equal to $11$

Answer

$11$

Do you know what the answer is?

Question 1

Is DE side in one of the triangles?

Question 2

True or false:

AB is a side of the triangle ABC.

Question 3

True or false:

AD is a side of triangle ABC.

Examples with solutions for The sides or edges of a triangle

Exercise #1

True or false:

DE not a side in any of the triangles.

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?

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.

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.

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.

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:
- $AB$ , connecting points A and B;
- $BC$ , connecting points B and C; and
- $CA$ , 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

Start practice

The sides or edges of a triangle

The sides of a triangle

types of triangles based on the sides:

Perimeter of a Triangle

Relation between the sides and the angles in a triangle

Can every three lines form a triangle?

Test yourself on parts of a triangle!

Perimeter of the triangle

A condition satisfied by the measures of the sides (or edges) of a triangle.

Examples of the subject

Example 1

Example 2

Example 3

Example 4

Questions on the subject

Exercises on the sides or edges of a triangle

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Examples with solutions for The sides or edges of a triangle

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Parts of a Triangle