All three medians in a triangle intersect at a single point called the centroid - If two medians intersect at a point inside the triangle, the third median must pass through it as well.
The intersection point of the medians - the centroid - divides each median in a ratio of 2:1 where the larger part of the median is closer to the vertex.
To which side(s) are the median and the altitude drawn?
Incorrect
Correct Answer:
BC
Question 4
The triangle ABC is shown below.
Which line segment is the median?
Incorrect
Correct Answer:
BE
Question 5
Look at triangle ABC below.
What is the median of the triangle and to which side is it drawn?
Incorrect
Correct Answer:
BE for AC
Examples with solutions for Parts of a Triangle
Exercise #1
True or false:
DE not a side in any of the triangles.
Video Solution
Step-by-Step Solution
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:
Identify triangles in the diagram. The diagram presented forms a right-angled triangle ABC with additional lines forming smaller triangles within.
Notice that while point D is used, the segment DE is only part of line BE and isn't listed as a direct side of any triangle.
Therefore, the claim that DE is not a side in any of the triangles is indeed correct.
Hence, the answer is True.
Answer
True
Exercise #2
Is DE side in one of the triangles?
Video Solution
Step-by-Step Solution
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.
Answer
Not true
Exercise #3
The triangle ABC is shown below.
To which side(s) are the median and the altitude drawn?
Step-by-Step Solution
To solve the problem of identifying to which side of triangle ABC the median and the altitude are drawn, let's analyze the diagram given for triangle ABC.
We acknowledge that a median is a line segment drawn from a vertex to the midpoint of the opposite side. An altitude is a line segment drawn from a vertex perpendicular to the opposite side.
Upon reviewing the diagram of triangle ABC, line segment AD is a reference term. It appears to meet point C in the middle, suggesting it's a median, but it also forms right angles suggesting it is an altitude.
Given the placement and orientation of AD, it is perpendicular to line BC (the opposite base for the median from A). Therefore, this line is both the median and the altitude to side BC.
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 BC, corresponding with choice Option 2: BC.
Answer
BC
Exercise #4
The triangle ABC is shown below.
Which line segment is the median?
Video Solution
Step-by-Step Solution
To solve this problem, we need to identify the median in triangle ABC:
Step 1: Recall the definition of a median. A median is a line segment drawn from a vertex to the midpoint of the opposite side.
Step 2: Begin by evaluating each line segment based on the definition.
Step 3: Identify points on triangle ABC:
AD is from A to a point on BC.
BE is from B to a point on AC.
FC is from F to a point on AB.
Step 4: Determine if these points (D, E, F) are midpoints:
Since BE connects B to E, and E is indicated to be the midpoint of segment AC (as shown), BE is the median.
AD and FC, by visual inspection, do not connect to midpoints on BC or AB respectively.
Therefore, the line segment that represents the median is BE.
Thus, the correct answer is: BE
Answer
BE
Exercise #5
Look at triangle ABC below.
What is the median of the triangle and to which side is it drawn?
Step-by-Step Solution
A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. In triangle △ABC, 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 E is located on side AC. If E is the midpoint of AC, then any line from a vertex to point E would be a median.
Step 3: Check line segment BE. This line runs from vertex B to point E.
Step 4: Since E is labeled as the midpoint of AC, line BE is the median of △ABC drawn to side AC.
Therefore, the median of the triangle is BE for AC.
Answer
BE for AC
Question 1
Look at triangle ABC below.
Which is the median?
Incorrect
Correct Answer:
EC
Question 2
Look at the triangle ABC below.
\( AD=\frac{1}{2}AB \)
\( BE=\frac{1}{2}EC \)
What is the median in the triangle?
Incorrect
Correct Answer:
DC
Question 3
ABC is a triangle.
What is the median of the triangle?
Incorrect
Correct Answer:
EC
Question 4
Look at the triangles in the figure.
Which line is the median of triangle ABC?
Incorrect
Correct Answer:
AG
Question 5
What is the median of triangle ABC?
Incorrect
Correct Answer:
CF
Exercise #6
Look at triangle ABC below.
Which is the median?
Step-by-Step Solution
To solve this problem, we must identify which line segment in triangle ABC is the median.
First, review the definition: a median in a triangle connects a vertex to the midpoint of the opposite side. Now, in triangle ABC:
Point A represents the vertex.
Point E lies on line segment AB.
Line segment EC needs to be checked to see if it connects vertex E to point C.
From the diagram, it appears that E is indeed the midpoint of side AB. Thus, line segment EC connects vertex C to this midpoint.
This fits the definition of a median, verifying that EC is the median line segment in triangle ABC.
Therefore, the solution to the problem is: EC.
Answer
EC
Exercise #7
Look at the triangle ABC below.
AD=21AB
BE=21EC
What is the median in the triangle?
Step-by-Step Solution
A median in a triangle is a line segment connecting a vertex to the midpoint of the opposite side. Here, we need to find such a segment in triangle △ABC.
Let's analyze the given conditions:
AD=21AB: Point D is the midpoint of AB.
BE=21EC: Point E is the midpoint of EC.
Given that D is the midpoint of AB, if we consider the line segment DC, it starts from vertex D and ends at C, passing through the midpoint of AB (which is D), fulfilling the condition for a median.
Therefore, the line segment DC is the median from vertex A to side BC.
In summary, the correct answer is the segment DC.
Answer
DC
Exercise #8
ABC is a triangle.
What is the median of the triangle?
Step-by-Step Solution
To solve the problem of identifying the median of triangle △ABC, we follow these steps:
Step 1: Understand the Definition - A median of a triangle is a line segment that extends from a vertex to the midpoint of the opposite side.
Step 2: Identify Potential Medians - Examine segments from each vertex to the opposite side. The diagram labels these connections.
Step 3: Confirm the Median - Specifically check the segment EC in the context of the line segment from vertex E to the side AC, and verify it reaches the midpoint of side AC.
Step 4: Verify Against Options - Given choices allow us to consider which point-to-point connection adheres to our criterion for a median. EC is given as one of the choices.
Observation shows: From point E (assumed from the label and position) that line extends directly to point C—a crucial diagonal opposite from considered midpoint indications, suggesting it cuts AC evenly, classifying it as a median.
Upon reviewing the given choices, we see that segment EC is listed. Confirming that EC indeed meets at C, the midpoint of AC, validates that it is a true median.
Therefore, the correct median of △ABC is the segment EC.
Answer
EC
Exercise #9
Look at the triangles in the figure.
Which line is the median of triangle ABC?
Step-by-Step Solution
To determine the median of triangle ABC, we need to identify the line that extends from one vertex to the midpoint of the opposite side.
Step 1: Review the given line segments in the figure.
Step 2: Recall that a median connects a vertex to the midpoint of the opposite side.
Step 3: Examine each line in the context of △ABC.
Let's consider each given line:
Line AF does not appear to connect to the midpoint of any side of the triangle directly.
Line DE is an internal line and does not serve as a median of the main triangle ABC.
Line FE is similar to DE, serving non-median purposes interior to another structure.
Line AG starts at vertex A and extends to point G, lying on side BC. If G is the midpoint of BC, then AG qualifies as the median.
Verification: Point G is positioned directly between points B and C along line BC, confirming its role as the midpoint.
Thus, the line AG is indeed the median of triangle ABC since it fulfills connecting vertex A and the midpoint of side BC.
Therefore, the solution to the problem is AG as the median of triangle ABC.
Answer
AG
Exercise #10
What is the median of triangle ABC?
Step-by-Step Solution
To determine the median of triangle ABC, we must identify a segment connecting a vertex of the triangle to the midpoint of the opposite side.
Examining the diagram, point F appears to be located on side AC. Given the configuration, point F divides side AC into two equal segments, which makes F the midpoint of AC.
Therefore, segment CF connects vertex C to the midpoint F of side AC. This characteristic aligns with the definition of a median in a triangle.
Hence, the median of triangle ABC is CF.
Answer
CF
Question 1
What is the median of triangle ABC.
Incorrect
Correct Answer:
There is no median shown.
Question 2
Look at the triangle ABC below.
Which of the following lines is the median of the triangle?
Incorrect
Correct Answer:
AD
Question 3
Look at the triangle ABC below.
Which of the line segments is the median?
Incorrect
Correct Answer:
FC
Question 4
True or false:
AB is a side of the triangle ABC.
Incorrect
Correct Answer:
True
Question 5
True or false:
AD is a side of triangle ABC.
Incorrect
Correct Answer:
Not true
Exercise #11
What is the median of triangle ABC.
Step-by-Step Solution
In this problem, we must determine if any of the line segments drawn within triangle ABC represent a median. A median is defined as a line segment extending from a vertex to the midpoint of the opposite side.
Upon examining the geometry of triangle ABC presented in the diagram:
The segment extending from A to the base BC and those depicted from B or C should be checked if they connect to a midpoint on the opposite side.
To be considered a median, a line from a vertex must bisect the opposite side into two equal lengths.
None of the segments drawn directly bisect the opposite sides they connect to, as evidenced by either lack of midpoint marking or unequal line segment sections along BC, CA, or AB.
Therefore, after careful inspection, there is no median shown in the given diagram.
Answer
There is no median shown.
Exercise #12
Look at the triangle ABC below.
Which of the following lines is the median of the triangle?
Step-by-Step Solution
To solve this problem, we apply the definition of a median in a triangle. A median is a line segment drawn from a vertex to the midpoint of the opposite side. In the diagram of the triangle ABC:
Line AD originates from vertex A and is directed towards point D on side BC.
We need to check if D is the midpoint of BC.
Given that AD meets the definition of a median by dividing BC into two equal segments, it is indeed the median.
After evaluating the possible choices:
Choice 1: AD is a line from A to the midpoint of BC.
Choice 2: AE doesn't bisect any side.
Choice 3: EC is not a median.
Choice 4: AC does not connect a vertex to a midpoint of the opposite side.
Therefore, the solution to the problem is that line segment AD is the median of triangle ABC.
Answer
AD
Exercise #13
Look at the triangle ABC below.
Which of the line segments is the median?
Step-by-Step Solution
To identify the median in triangle ABC, we will utilize the definition of a median: it is the line segment extending from a vertex of the triangle to the midpoint of the opposite side.
In the diagram, triangle ABC is formed with vertices A, B, and C. We need to identify which of the segments is drawn from a vertex and intersects the opposite side at its midpoint.
Examine segment FC:
F appears to be a midpoint of side AB of the triangle ABC.
Line segment FC originates from vertex C and extends to F.
The segment FC meets the criteria for a median as it connects vertex C to the midpoint of AB.
Therefore, we conclude that the median of triangle ABC is FC.
Answer
FC
Exercise #14
True or false:
AB is a side of the triangle ABC.
Video Solution
Step-by-Step Solution
To solve this problem, let's clarify the role of AB in the context of triangle ABC by analyzing its diagram:
Step 1: Identify the vertices of the triangle. According to the diagram, the vertices of the triangle are points labeled A, B, and C.
Step 2: Determine the sides of the triangle. In any triangle, the sides are the segments connecting pairs of distinct vertices.
Step 3: Identify AB as a line segment connecting vertex A and vertex B, labeled directly in the diagram.
Considering these steps, line segment AB connects vertex A with vertex B, and hence, forms one of the sides of the triangle ABC. Therefore, AB is indeed a side of triangle ABC as shown in the diagram.
The conclusion here is solidly supported by our observation of the given triangle. Thus, the statement that AB is a side of the triangle ABC is True.
Answer
True
Exercise #15
True or false:
AD is a side of triangle ABC.
Video Solution
Step-by-Step Solution
To determine if line segment AD is a side of triangle ABC, we need to agree on the definition of a triangle's side. A triangle consists of three sides, each connecting pairs of its vertices. In triangle ABC, these sides are AB, BC, and CA. Each side is composed of a direct line segment connecting the listed vertices.
In the diagram provided, there is no indication of a point D connected to point A or any other vertex of triangle ABC. To claim AD as a side, D would need to be one of the vertices B or C, or a commonly recognized point forming part of the triangle’s defined structure. The provided figure and description do not support that AD exists within the given triangle framework, as no point D is defined within or connecting any existing vertices.
Therefore, according to the problem's context and based on the definition of the sides of a triangle, AD cannot be considered a side of triangle ABC. It follows that the statement "AD is a side of triangle ABC" should be deemed not true.