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Properties of triangles

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Properties of triangles

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In this presentation, we will explore the concept of triangle, types of triangles, their properties and area of ​​triangle. We will see how they are classified, what relationships exist between their sides and angles.

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Paradiso Indra
Paradiso Indra
India
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Properties of triangles
 

Properties of trianglesOnline version

In this presentation, we will explore the concept of triangle, types of triangles, their properties and area of ​​triangle. We will see how they are classified, what relationships exist between their sides and angles.

by Paradiso Indra
1

What is a triangle?

A triangle is a flat geometric figure that is made up of three straight sides that meet at three points called vertices. It is the simplest and most basic polygonal figure, and is the basis for constructing other more complex figures.

 

Elements of a triangle:

 

Sides: They are the line segments that form the triangle.

Vertices: These are the points where the sides of the triangle meet.

Angles: They are the openings formed by two sides that meet at a vertex.

2

According to its sides

Equilateral

It has three equal sides and therefore, the three angles also measure 60 degrees


Isosceles

It has two equal sides and the angles opposite to those sides are also equal.


Scalene

All its sides have different lengths and, consequently, all its angles are also different.

3

According to their angles

Acutangle:

All its interior angles measure less than 90 degrees.


Rectangle:

It has an interior angle that measures exactly 90 degrees (right angle). The other two angles are acute.


Obtuse angle:

It has an interior angle that measures more than 90 degrees (obtuse angle). The other two angles are acute.

4

Relationships between Sides and Angles

Sides opposite equal angles:

in an isósceles triangle, the sides opposite equal angles have tha same length.


Angles opposite equal sides:

in an equilateral triangle, the angles opposite equal sides have the same measure.


Pythagorean theorem:

in a right triangle, the square of the hypotenuse ( the side opposite the right angle) is equal to the sum of the squares of the lens ( the other two sides).

5

Triangle Area

the area of a triangle is calculated using the following formula:

area: ( base * height) / 2


Base:

any side of the triangle can be considered as the base.


HEIGHT:

the perpendicular distance from the vertex opposite the base to the line containing the base.

6

Introduction to Triangles

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the simplest shapes in geometry.

Triangles can be classified based on:

  • Sides: Equilateral, Isosceles, Scalene
  • Angles: Acute, Right, Obtuse
7

Types of Triangles by Sides

Classification by Sides

Triangles can be categorized into three types based on the lengths of their sides:

  • Equilateral Triangle: All three sides are equal.
  • Isosceles Triangle: Two sides are equal, and the angles opposite those sides are equal.
  • Scalene Triangle: All sides are of different lengths.
8

Types of Triangles by Angles

Classification by Angles

Triangles can also be classified based on their angles:

  • Acute Triangle: All angles are less than 90 degrees.
  • Right Triangle: One angle is exactly 90 degrees.
  • Obtuse Triangle: One angle is greater than 90 degrees.
9

Triangle Properties

Key Properties of Triangles

Triangles have several important properties:

  • The sum of the interior angles is always 180 degrees.
  • The longest side is opposite the largest angle.
  • The shortest side is opposite the smallest angle.
10

Triangle Inequality Theorem

Understanding the Triangle Inequality Theorem

This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In mathematical terms:

  • a + b > c
  • a + c > b
  • b + c > a
11

Area of a Triangle

Calculating the Area

The area of a triangle can be calculated using the formula:

Area = 1/2 × base × height

Where:

  • Base: The length of the bottom side.
  • Height: The perpendicular distance from the base to the opposite vertex.
12

Perimeter of a Triangle

Calculating the Perimeter

The perimeter of a triangle is the sum of the lengths of all its sides:

Perimeter = a + b + c

Where a, b, and c are the lengths of the sides.

13

Real-Life Applications of Triangles

Where Do We See Triangles?

Triangles are everywhere in our daily lives:

  • Architecture: Triangles provide stability in structures.
  • Engineering: Used in trusses and bridges.
  • Art: Triangles are often used in designs and patterns.
14

Fun Facts About Triangles

Interesting Triangle Facts

Here are some fun facts:

  • The largest triangle in the world is the Great Pyramid of Giza.
  • Triangles are the strongest shape in construction.
  • Every triangle can be inscribed in a circle.
 
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