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:
True or false:
DE not a side in any of the triangles.
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 DE side in one of the triangles?
The triangle ABC is shown below.
To which side(s) are the median and the altitude drawn?
The triangle ABC is shown below.
Which line segment is the median?
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 .
Look at triangle ABC below.
What is the median of the triangle and to which side is it drawn?
Look at triangle ABC below.
Which is the median?
Look at the triangle ABC below.
\( AD=\frac{1}{2}AB \)
\( BE=\frac{1}{2}EC \)
What is the median in the triangle?
True or false:
DE not a side in any of the triangles.
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:
Therefore, the claim that DE is not a side in any of the triangles is indeed correct.
Hence, the answer is True.
True
Is DE side in one of the triangles?
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.
Not true
The triangle ABC is shown below.
To which side(s) are the median and the altitude drawn?
To solve the problem of identifying to which side of triangle the median and the altitude are drawn, let's analyze the diagram given for triangle .
Thus, the side to which both the median and the altitude are drawn is BC.
Therefore, the correct answer to the problem is the side , corresponding with choice .
BC
The triangle ABC is shown below.
Which line segment is the median?
To solve this problem, we need to identify the median in triangle ABC:
Therefore, the line segment that represents the median is .
Thus, the correct answer is: BE
BE
Look at triangle ABC below.
What is the median of the triangle and to which side is it drawn?
A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. In triangle , we need to identify such a median from the diagram provided.
Step 1: Observe the diagram to identify the midpoint of each side.
Step 2: It is given that point is located on side . If is the midpoint of , then any line from a vertex to point would be a median.
Step 3: Check line segment . This line runs from vertex to point .
Step 4: Since is labeled as the midpoint of , line is the median of drawn to side .
Therefore, the median of the triangle is for .
BE for AC