Parts of a Triangle - Examples, Exercises and Solutions

Question Types:
Parts of a Triangle: Calculate Angles in QuadrilateralsParts of a Triangle: Classify a triangle by its sidesParts of a Triangle: Determine the size of the given anglesParts of a Triangle: Finding the size of angles in a triangleParts of a Triangle: Identifying and defining elementsParts of a Triangle: Identifying sides in a triangleParts of a Triangle: Identifying the sides in a triangle using median and heightParts of a Triangle: Identify the greater valueParts of a Triangle: Is it possible...?Parts of a Triangle: Median in an isosceles triangle - propertiesParts of a Triangle: Median in a right-angled triangleParts of a Triangle: True / falseParts of a Triangle: Using angles in a triangleParts of a Triangle: Using parallel linesParts of a Triangle: Using properties of the medianParts of a Triangle: Using the median to calculate the perimeterParts of a Triangle: Using the theorem: The median of a triangle divides it into two triangles of the same area

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.

Detailed explanation

Practice Parts of a Triangle

Question 1

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCEEEDDD

Question 2

Which of the following is the height in triangle ABC?

AAABBBCCCDDD

Question 3

ABC is an isosceles triangle.

AD is the median.

What is the size of angle \( ∢\text{ADC} \)?

AAABBBCCCDDD

Question 4

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

Question 5

Can a triangle have two right angles?

Examples with solutions for Parts of a Triangle

Exercise #1

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCEEEDDD

Video Solution

Step-by-Step Solution

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.

Answer

AE

Exercise #2

Which of the following is the height in triangle ABC?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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.

Answer

AB

Exercise #3

ABC is an isosceles triangle.

AD is the median.

What is the size of angle ∢ADC ∢\text{ADC} ?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

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.

Answer

90

Exercise #4

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

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.

Answer

No

Exercise #5

Can a triangle have two right angles?

Video Solution

Step-by-Step Solution

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.

Answer

No

Question 1

True or false?

\( \alpha+\beta=180 \)

αβ

Question 2

Three angles measure as follows: 60°, 50°, and 70°.

Is it possible that these are angles in a triangle?

Question 3

Tree angles have the sizes:

76°, 52°, and 52°.

Is it possible that these angles are in a triangle?

Question 4

Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a triangle?

Question 5

Tree angles have the sizes:

69°, 93°, and 81.

Is it possible that these angles are in a triangle?

Exercise #6

True or false?

α+β=180 \alpha+\beta=180

αβ

Video Solution

Step-by-Step Solution

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.

Answer

True

Exercise #7

Three angles measure as follows: 60°, 50°, and 70°.

Is it possible that these are angles in a triangle?

Video Solution

Step-by-Step Solution

Recall that the sum of angles in a triangle equals 180 degrees.

Let's add the three angles to see if their sum equals 180:

60+50+70=180 60+50+70=180

Therefore, it is possible that these are the values of angles in some triangle.

Answer

Possible.

Exercise #8

Tree angles have the sizes:

76°, 52°, and 52°.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

We will add the three angles to find out if their sum equals 180:

76+52+52=180 76+52+52=180

Therefore, these could be the values of angles in some triangle.

Answer

Yes.

Exercise #9

Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

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:

94+36.5+49.5=180 94+36.5+49.5=180

Therefore, these could be the values of angles in some triangle.

Answer

Possible.

Exercise #10

Tree angles have the sizes:

69°, 93°, and 81.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

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:

69+81+93=243 69+81+93=243

Therefore, these cannot be the values of angles in any triangle.

Answer

No.

Question 1

Tree angles have the sizes:

90°, 60°, and 40.

Is it possible that these angles are in a triangle?

Question 2

Tree angles have the sizes:

50°, 41°, and 81.

Is it possible that these angles are in a triangle?


Question 3

Tree angles have the sizes:

90°, 60°, and 30.

Is it possible that these angles are in a triangle?

Question 4

Tree angles have the sizes:

31°, 122°, and 85.

Is it possible that these angles are in a triangle?

Question 5

If a tree's angles are sizes 56°, 89°, and 17°.

Is it possible that these angles are in a triangle?

Exercise #11

Tree angles have the sizes:

90°, 60°, and 40.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

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:

90+60+40=190 90+60+40=190

Therefore, these cannot be the values of angles in any triangle.

Answer

Yes.

Exercise #12

Tree angles have the sizes:

50°, 41°, and 81.

Is it possible that these angles are in a triangle?


Video Solution

Step-by-Step Solution

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:

50+41+81=172 50+41+81=172

Therefore, these cannot be the values of angles in any triangle.

Answer

Impossible.

Exercise #13

Tree angles have the sizes:

90°, 60°, and 30.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

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:

90+60+30=180 90+60+30=180

Therefore, these could be the values of angles in some triangle.

Answer

No.

Exercise #14

Tree angles have the sizes:

31°, 122°, and 85.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

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:

31+122+85=238 31+122+85=238

Therefore, these cannot be the values of angles in any triangle.

Answer

Impossible.

Exercise #15

If a tree's angles are sizes 56°, 89°, and 17°.

Is it possible that these angles are in a triangle?

Video Solution

Step-by-Step Solution

Let's calculate the sum of the angles to see what total we get in this triangle:

56+89+17=162 56+89+17=162

The sum of angles in a triangle is 180 degrees, so this sum is not possible.

Answer

Impossible.

More Questions

Topics learned in later sections

  1. Area
  2. The sides or edges of a triangle
  3. Triangle Height
  4. The Sum of the Interior Angles of a Triangle
  5. Exterior angles of a triangle
  6. Types of Triangles
  7. Obtuse Triangle
  8. Equilateral triangle
  9. Identification of an Isosceles Triangle
  10. Scalene triangle
  11. Acute triangle
  12. Isosceles triangle
  13. The Area of a Triangle
  14. Area of a right triangle
  15. Area of Isosceles Triangles
  16. Area of a Scalene Triangle
  17. Area of Equilateral Triangles
  18. Areas of Polygons for 7th Grade
  19. Right Triangle
  20. Height in a triangle
  21. Center of a Triangle - The Centroid - The Intersection Point of Medians
  22. How do we calculate the area of complex shapes?
  23. How to calculate the area of a triangle using trigonometry?
  24. Perimeter
  25. Triangle
  26. Perimeter of a triangle
  27. How do we calculate the perimeter of polygons?