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!

Is DE side in one 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

Determine the type of angle given.

Question 2

Determine the type of angle given.

Question 3

Is the straight line in the figure the height of the triangle?

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

Is the straight line in the figure the height of the triangle?

Question 2

Is the straight line in the figure the height of the triangle?

Question 3

Is the straight line in the figure the height of the triangle?

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

Is the straight line in the figure the height of the triangle?

Question 2

Is the straight line in the figure the height of the triangle?

Question 3

The triangle ABC is shown below.

Which line segment is the median?

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

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.

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

Given the following triangle:

Write down the height of the triangle ABC.

Question 2

Can a triangle have a right angle?

Question 3

Is DE side in one 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

Determine the type of angle given.

Question 2

Determine the type of angle given.

Question 3

Is the straight line in the figure the height of the triangle?

Examples with solutions for The sides or edges of a triangle

Exercise #1

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 #2

Determine the type of angle given.

Video Solution

Step-by-Step Solution

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.

Answer

Right

Exercise #3

Determine the type of angle given.

Video Solution

Step-by-Step Solution

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.

Answer

Straight

Exercise #4

Is the straight line in the figure the height of the triangle?

Video Solution

Step-by-Step Solution

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.

Answer

Yes

Exercise #5

Is the straight line in the figure the height of the triangle?

Video Solution

Step-by-Step Solution

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.

Answer

Yes

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