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:
AB is a side in triangle ADB
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
According to figure BC=CB?
Can a plane angle be found in a triangle?
Can a triangle have a right angle?
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 .
Can a triangle have two right angles?
DB is a side in triangle ABC
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
In an isosceles triangle, the angle between ? and ? is the "base angle".
An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."
Therefore, the correct choice is Side, base.
Side, base.
Look at the two triangles below. Is EC a side of one of the triangles?
Every triangle has 3 sides. First let's go over the triangle on the left side:
Its sides are: AB, BC, and CA.
This means that in this triangle, side EC does not exist.
Let's then look at the triangle on the right side:
Its sides are: ED, EF, and FD.
This means that in this triangle, side EC also does not exist.
Therefore, EC is not a side in either of the triangles.
No
According to figure BC=CB?
In geometry, the distance or length of a line segment between two points is the same, regardless of the direction in which it is measured. Consequently, the segments denoted by and refer to the same segment, both indicating the distance between points B and C.
Hence, the statement "BC = CB" is indeed True.
True
Look at the two triangles below.
Is CB a side of one of the triangles?
In order to determine if segment CB is a side of one of the triangles, let's start by identifying the triangles and their corresponding vertices from the given diagram:
Now, to decide if CB is a side, we need to check if a line segment exists between points C and B in any of these triangles.
Upon examining the points:
Therefore, segment CB is indeed a side of triangle ABC, confirming that the answer is Yes.
Thus, the solution to the problem is .
Yes.
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
In order to solve this problem, we need to understand the basic properties of an isosceles triangle.
An isosceles triangle has two sides that are equal in length, often referred to as the "legs" of the triangle. The angle formed between these two equal sides, which are sometimes referred to as the "sides", is called the "vertex angle" or sometimes more colloquially as the "main angle".
When considering the vocabulary of the given multiple-choice answers, choice 2: accurately fills the blanks, as the angle formed between the two equal sides can indeed be referred to as the "main angle".
Therefore, the correct answer to the problem is: .
sides, main