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:
Given the following triangle:
Write down the height of the triangle ABC.
Look at the two triangles below. Is EC a side of one of the triangles?
ABC is an isosceles triangle.
AD is the median.
What is the size of angle \( ∢\text{ADC} \)?
Which of the following is the height in triangle ABC?
Can a triangle have two right angles?
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
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
ABC is an isosceles triangle.
AD is the median.
What is the size of angle ?
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
Which of the following is the height in triangle ABC?
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
Can a triangle have two right angles?
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.
No
True or false?
\( \alpha+\beta=180 \)
Find the measure of the angle \( \alpha \)
If a tree's angles are sizes 56°, 89°, and 17°.
Is it possible that these angles are in a triangle?
Find the measure of the angle \( \alpha \)
Find the measure of the angle \( \alpha \)
True or false?
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
Find the measure of the angle
It is known that the sum of angles in a triangle is 180 degrees.
Since we are given two angles, we can calculate
We should note that the sum of the two given angles is greater than 180 degrees.
Therefore, there is no solution possible.
There is no possibility of resolving
If a tree's angles are sizes 56°, 89°, and 17°.
Is it possible that these angles are in a triangle?
Let's calculate the sum of the angles to see what total we get in this triangle:
The sum of angles in a triangle is 180 degrees, so this sum is not possible.
Impossible.
Find the measure of the angle
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
Therefore, we will use the following formula:
Now let's input the known data:
We'll move the term to the other side and keep the appropriate sign:
33
Find the measure of the angle
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
Therefore, we will use the following formula:
Now let's input the known data:
We'll move the term to the other side and keep the appropriate sign:
88
Tree angles have the sizes:
31°, 122°, and 85.
Is it possible that these angles are in a triangle?
Tree angles have the sizes:
50°, 41°, and 81.
Is it possible that these angles are in a triangle?
Tree angles have the sizes:
69°, 93°, and 81.
Is it possible that these angles are in a triangle?
Tree angles have the sizes:
90°, 60°, and 30.
Is it possible that these angles are in a triangle?
Tree angles have the sizes:
90°, 60°, and 40.
Is it possible that these angles are in a triangle?
Tree angles have the sizes:
31°, 122°, and 85.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these cannot be the values of angles in any triangle.
Impossible.
Tree angles have the sizes:
50°, 41°, and 81.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these cannot be the values of angles in any triangle.
Impossible.
Tree angles have the sizes:
69°, 93°, and 81.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these cannot be the values of angles in any triangle.
No.
Tree angles have the sizes:
90°, 60°, and 30.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these could be the values of angles in some triangle.
No.
Tree angles have the sizes:
90°, 60°, and 40.
Is it possible that these angles are in a triangle?
Let's remember that the sum of angles in a triangle is equal to 180 degrees.
We'll add the three angles to see if their sum equals 180:
Therefore, these cannot be the values of angles in any triangle.
Yes.