The sides or edges of a triangle - Examples, Exercises and Solutions

Every triangle has three sides. The sides allow us to classify the different types of triangles according to their size.

For example, a triangle with two equal sides (edges) is an isosceles triangle and one in which all its sides (edges) are equal is an equilateral triangle. While a triangle that has all its sides different is an equilateral triangle.

examples with solutions for the sides or edges of a triangle

Exercise #1

Given the following triangle:

Write down the height of the triangle ABC.

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 drawing, we can notice that the previous theorem is true for the line AE that crosses BC and forms a 90-degree angle, comes out of vertex A and therefore is the altitude of the triangle.

Answer

AE

Exercise #2

ABC is an isosceles triangle.

AD is the median.

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

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 #3

Which of the following is the height in triangle ABC?

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 #4

True or false?

$\alpha+\beta=180$

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 #5

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:

$60+50+70=180$

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