# Triangles

Tri = 3
Angle = Angle !

The sum of the interior angles of a triangle is 180 degrees.

If you place each angle side by side, you will see that they form a straight angle. No matter how the triangle is, the sum of its interior angles is 180 degrees. There are other proof methods to show it's 180 degrees, but that's beyond our current topic.

# Classification of Triangles

## Based on Side Lengths

Equilateral Triangle: All three sides are of equal length.
The term "equilateral" is derived from the Latin words "aequus" meaning "equal" and "latus" meaning "side." Thus, "equilateral" essentially translates to "equal sides."

An "Equilateral Triangle" in geometry is a triangle in which all three sides are of equal length. Due to this equality in side lengths, all of the interior angles of an equilateral triangle are also equal. Each angle measures 60 degrees, making the total sum of the angles 180 degrees, as is the case with all triangles.

Isosceles Triangle: Exactly two sides are of equal length.

The term "isosceles" comes from the Ancient Greek words "isos" meaning "equal" and "skelos" meaning "leg." Therefore, "isosceles" essentially means "equal legs."

An "Isosceles Triangle" in geometry is a triangle that has two sides of equal length. These two equal sides are often referred to as the "legs" of the triangle, while the third side is called the "base." The angles opposite the equal sides are also equal to each other. This means that an isosceles triangle has both symmetry in terms of side lengths and angles.

Scalene Triangle: All three sides have different lengths.

The term "scalene" originates from the Latin word "scaenus," which means "leg." However, in the context of triangles, the term relates to the idea that the triangle has three distinct "legs" or sides. In other words, a scalene triangle has three sides of different lengths.

In English, the term "scalene triangle" is used to describe triangles where all three sides are of different lengths. This means the triangle doesn't have any sides of equal length. Thus, the term "scalene" emphasizes the unique and unbalanced nature of such a triangle.

# Based on Interior Angles

Obtuse Triangle: One interior angle is greater than 90 degrees.
Acute Triangle: All interior angles are less than 90 degrees.
Right Triangle: One interior angle is exactly 90 degrees.

When classifying triangles, you seem to fall into the misconception that only one characteristic will be considered in a triangle. We classify based on different features, one being the side and the other being the angle. For example, you can classify students by hair color (red, black, blonde, etc.) or by whether they wear glasses. A student can be both red-haired and wear glasses, so a triangle can be both scalene and have different angles. The angle property is distinct from the side property.

# Side-Angle Relationship

Imagine a triangle with a fixed base, and its right and left sides connected to a red pin at the top by a string. The red point on top should be able to move in the same direction.

When we move the red point, the short side lengthens while the long side starts to shorten.

When the red dot comes to the midpoint of the base, the lengths of the right and left edges become equal. That is, the distance of the red dot to the right end point is the same as its distance to the left end point.

Let's look at the relationship between the angle and the side;

Let A and B be our angles; it is clear that angle A is larger than angle B.

When I move the red dot, angle A starts to narrow while angle B begins to enlarge.

When the red dot aligns with the exact direction of the midpoint, angles A and B become equal. This tells us that in an isosceles triangle, the angles on the congruent sides are the same.

Let's explain it again from a different perspective.

it is you :)

AB < BC

If you extend one arm more than the other, the distance from the direction of the arm you opened wider to your body will be greater than the distance from the arm you opened less.

If you open your arms equally, that is, if the red angles are equal to each other, then AB will be equal to BC.
In this case, we need to show whether the blue angles are equal or not, as you know the sum of the interior angles of a triangle is 180 degrees. For the 1st triangle; 90 degrees + red angle + blue angle = 180 degrees. Similarly, for the 2nd triangle; 90 degrees + red angle + blue angle = 180 degrees. This situation can occur if the blue angles are equal to each other.

Result;

## in an isosceles triangle, the angles on the congruent sides are equal to each other.

This method is very useful for drawing perpendicular lines from a point.How ?

Using an isosceles triangle, can you demonstrate that one angle of an equilateral triangle is 60 degrees?

This method is very useful for drawing perpendicular lines from a point.How ?