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.
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
21cm=3x
x=21cm:3
Answer:
x=7cm
Example 4
Tell if it is possible to construct a triangle in which its sides measure 5cm, 7cm and 10cm.
Solution
We add the lengths of any two sides (edges) and compare with the length of the remaining side.
5cm+7cm=12cmwhich is greater than the remaining side that measures 10cm
7cm+10cm=17cmThe length of the remaining side, which is greater than the remaining side measuring 5cm, is greater than the remaining side measuring 5cm.
10cm+5cm=15cm, which is greater than the remaining side measuring 7cm.
Answer:
So if it is possible to construct a triangle of measures 5cm, 7cm and 10cm on each side.
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 △DBC but DE ends at the point E which is not an angle in any of the triangles in the figure.
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
8.58.5X=X=8.517=2
Answer
2
Exercise 5
Request
Given the equilateral triangle
The perimeter of the triangle is 33cm, 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
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 ∢ADC?
Video Solution
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.
Answer
90
Exercise #2
Given the following triangle:
Write down the height of the triangle ABC.
Video Solution
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 image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.
Answer
AE
Exercise #3
Which of the following is the height in triangle ABC?
Video Solution
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.
Answer
AB
Exercise #4
Can a triangle have two right angles?
Video Solution
Step-by-Step Solution
The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.
Answer
No
Exercise #5
True or false?
α+β=180
Video Solution
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.