A median in a triangle is a line segment that extends from a vertex to the midpoint of the opposite side, dividing it into two equal parts.
A median in a triangle is a line segment that extends from a vertex to the midpoint of the opposite side, dividing it into two equal parts.
Additional properties:
Can a triangle have a right angle?
In this article, we will learn everything you need to know about medians in a triangle! Don't worry, the material about medians in a triangle is both easy and straightforward to understand.
A median in a triangle is a line segment that extends from a vertex to the midpoint of the opposite side, dividing it into two equal parts.
Remember that "median" in real life represents the middle point, and similarly here it divides the side in the middle!
We can observe this in the following drawing:
In triangle
is a median - it extends from the vertex and divides the opposite side into two
equal parts:
Additional Properties of a Median in a Triangle:
You can observe this below:
Since there are 3 vertices in a triangle, there can be 3 medians.
Each median extends from a vertex to the opposite side and bisects it.
All medians intersect at one point.
Reminder:
How do we calculate the area of a triangle?
If we take for example the triangle and want to calculate its area when:
height =
We can deduce that the area of triangle is:
Now if we draw the median we can observe that the two triangles it creates are equal in area.
The side is divided in the middle thus it is identical in both triangles and the height is identical.
Therefore, the area of each created triangle is identical and will be equal to half the area of triangle
Is the straight line in the figure the height of the triangle?
Is the straight line in the figure the height of the triangle?
Can a plane angle be found in a triangle?
is a median drawn from vertex angle .
It is also a height to side , as well as a median to , in addition to bisecting the vertex angle .
3. In a right triangle - the median to the hypotenuse equals half the hypotenuse.
We can observe this in the figure below:
Triangle is a right triangle.
is the median to the hypotenuse and equals half of the hypotenuse.
That is
Given:
is a median in triangle
is a median in triangle
Solution:
Given that –
Since is a median,
due to the fact that the median bisects the side at its midpoint.
Given that is also a median.
Therefore .
2. Given that the area of triangle is
The area of triangle
must also be . A median divides the triangle into two triangles of equal area.
3. The area of triangle must be equal to the area of triangle .
Triangle consists of two triangles with equal areas that sum up to .
Therefore, the area of triangle is .
Is the straight line in the figure the height of the triangle?
Is the straight line in the figure the height of the triangle?
Is the straight line in the figure the height of the triangle?
Determine the type of angle given.
To solve this problem, we'll examine the image presented for the angle type:
Now, let's apply these steps:
Step 1: Analyzing the provided diagram, observe that there is an angle formed among the segments.
Step 2: The angle is depicted with a measure that appears greater than a right angle (greater than ). It is wider than an acute angle.
Step 3: Given the definition of an obtuse angle (greater than but less than ), the graphic clearly shows an obtuse angle.
Therefore, the solution to the problem is Obtuse.
Obtuse
Given the following triangle:
Write down the height of the triangle ABC.
To resolve this problem, let's focus on recognizing the elements of the triangle given in the diagram:
Thus, the height of triangle is effectively identified as segment .
BD
Given the following triangle:
Write down the height of the triangle ABC.
To determine the height of triangle , we need to identify the line segment that extends from a vertex and meets the opposite side at a right angle.
Given the diagram of the triangle, we consider the base and need to find the line segment from vertex to this base.
From the diagram, segment is drawn from and intersects the line (or its extension) perpendicularly. Therefore, it represents the height of the triangle .
Thus, the height of is segment .
BD
Given the following triangle:
Write down the height of the triangle ABC.
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.
AE
Given the following triangle:
Write down the height of the triangle ABC.
To solve this problem, we need to identify the height of triangle ABC from the diagram. The height of a triangle is defined as the perpendicular line segment from a vertex to the opposite side, or to the line containing the opposite side.
In the given diagram:
The perpendicularity of to is illustrated by the right angle symbol at point . This establishes as the height of the triangle ABC.
Considering the options provided, the line segment that represents the height of the triangle ABC is indeed .
Therefore, the correct choice is: .
AD