All terms in triangle calculation

🏆Practice parts of a triangle

Terms used in triangle calculations

  • Line

A line is a general term for straight lines (hence its name) that extend from a specific point on the triangle.

  • Height

Height is a line that extends from a specific vertex and reaches perpendicularly to the opposite side, creating a right angle. The height is marked with the letter h (from the word height).

  • Median

The median is also a line extending from a specific vertex to the opposite side, but it reaches exactly the middle of the opposite side and divides it into two equal parts.

  • Angle Bisector

An angle bisector is a line that extends from a specific vertex and actually divides the vertex into two equal angles.

  • Perpendicular Bisector

A perpendicular bisector is a line that extends from the middle of a side perpendicular to it.

  • Midsegment

A midsegment is a line that connects the midpoints of two sides and is parallel to the third side, with its length being half of it.

  • Opposite Side

An opposite side is the side that is located opposite to a specific vertex and does not pass through it.

Diagram of a triangle ABC illustrating key geometric concepts: height (H) in green, median in blue, angle bisector in red, perpendicular bisector from CB in orange, midsegment in purple, and the side opposite to vertex A highlighted in orange. Labels are color-coded for clarity.

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Test yourself on parts of a triangle!

einstein

True or false:

DE not a side in any of the triangles.
AAABBBCCCDDDEEE

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Terms used in triangle calculations

Line

A ray is a general name for straight lines (hence its name) that extend from a specific point on the triangle.

Height

Height is a line that extends from a specific vertex and reaches perpendicularly to the opposite side, creating a right angle. Height is marked with the letter h (from the word height in English).

Median

The median is also a line that extends from a specific vertex to the opposite side, but it reaches exactly the middle of the opposite side and divides it into two equal parts.

Angle Bisector

An angle bisector is a line that extends from a specific vertex and divides the angle into two equal angles.

Perpendicular Bisector

A median perpendicular is a line that extends from the middle of a side perpendicular to it.

Midsegment

A midsegment is a line segment that connects the midpoints of two sides and is parallel to the third side, and its length is half of it.

Opposite Side

An opposite side is the side located across from a specific vertex and does not pass through it.

Diagram of a triangle ABC illustrating key geometric concepts: height (H) in green, median in blue, angle bisector in red, perpendicular bisector from CB in orange, midsegment in purple, and the side opposite to vertex A highlighted in orange. Labels are color-coded for clarity.

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Examples with solutions for Parts of a Triangle

Exercise #1

True or false:

DE not a side in any of the triangles.
AAABBBCCCDDDEEE

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.
  • Triangles formed: Triangle ABC (major triangle), Triangle ABD, Triangle BEC, and Triangle DBE.
  • Let's examine the sides of these triangles:
    • Triangle ABC has sides AB, BC, and CA.
    • Triangle ABD has sides AB, BD, and DA.
    • Triangle BEC has sides BE, EC, and CB.
    • Triangle DBE has sides DB, BE, and ED.
  • 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?
AAABBBCCCDDDEEE

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?

AAABBBCCCDDDEEEFFF

Step-by-Step Solution

To solve the problem of identifying to which side of triangle ABC ABC the median and the altitude are drawn, let's analyze the diagram given for triangle ABC 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 ABC , line segment AD AD is a reference term. It appears to meet point C 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 AD , it is perpendicular to line BC BC (the opposite base for the median from A A ). Therefore, this line is both the median and the altitude to side BC 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 BC , corresponding with choice Option 2: BC \text{Option 2: BC} .

Answer

BC

Exercise #4

The triangle ABC is shown below.

Which line segment is the median?

AAABBBCCCDDDEEEFFF

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 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?

AAABBBCCCDDDEEE

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 \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 E is located on side AC AC . If E E is the midpoint of AC AC , then any line from a vertex to point E E would be a median.

Step 3: Check line segment BE BE . This line runs from vertex B B to point E E .

Step 4: Since E E is labeled as the midpoint of AC AC , line BE BE is the median of ABC \triangle ABC drawn to side AC AC .

Therefore, the median of the triangle is BE BE for AC AC .

Answer

BE for AC

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