# The sides or edges of a triangle

🏆Practice parts of a triangle

Every triangle has three sides. The sides allow us to classify the different types of triangles according to their size.

For example, a triangle with two equal sides (edges) is an isosceles triangle and one in which all its sides (edges) are equal is an equilateral triangle. While a triangle that has all its sides different is an equilateral triangle.

## Test yourself on parts of a triangle!

True or false:

DE not a side in any of the triangles.

## 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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## 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,

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

$P=12\operatorname{cm}$

### 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.

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

Do you know what the answer is?

### 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.

$P=3x$

$21\operatorname{cm}=3x$

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

$x=7\operatorname{cm}$

### 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 $7~cm$.

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

## 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?

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.

True

Do you think you will be able to solve it?

### 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.

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.

Scalene triangle

### 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. $X$

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

$2$

### 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 $11$

$11$

Do you know what the answer is?

## examples with solutions for the sides or edges of a triangle

### Exercise #1

ABC is an isosceles triangle.

AD is the median.

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

### Step-by-Step Solution

In an isosceles triangle, the median to the base is also the height to the base.

That is, side AD forms a 90° angle with side BC.

That is, two right triangles are created.

Therefore, angle ADC is equal to 90 degrees.

90

### Exercise #2

Given the following triangle:

Write down the height of the triangle ABC.

### Step-by-Step Solution

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the drawing, we can notice that the previous theorem is true for the line AE that crosses BC and forms a 90-degree angle, comes out of vertex A and therefore is the altitude of the triangle.

AE

### Exercise #3

Which of the following is the height in triangle ABC?

### Step-by-Step Solution

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

AB

### Exercise #4

True or false?

$\alpha+\beta=180$

### Step-by-Step Solution

Given that the angles alpha and beta are on the same straight line and given that they are adjacent angles. Together they are equal to 180 degrees and the statement is true.

True

### Exercise #5

Three angles measure as follows: 60°, 50°, and 70°.

Is it possible that these are angles in a triangle?

### Step-by-Step Solution

Recall that the sum of angles in a triangle equals 180 degrees.

Let's add the three angles to see if their sum equals 180:

$60+50+70=180$

Therefore, it is possible that these are the values of angles in some triangle.