Triangles: definition and fundamental properties - 5th grade

 

properties of triangles

 

Triangles classification and properties

Ø  What is a triangle?

A triangle is a three-sided polygon. The notation that is usually used is to name their vertices with the capital letters A, B and C (but they can be other, as long as they are uppercase) and the sides opposite these vertices, with the respective lowercase letters, as shown in the image.

Ø  What are its most important properties?

Its three fundamental properties are:

1) The sum of its interior angles is 180º.

An example is the triangle in the following figure, where the mentioned sum and its result appear:

2) The sum of its exterior angles is 360º. Look at the following figure as an example of this property:

 

3) Each exterior angle of a triangle is equal to the sum of the two interior angles not adjacent to it (that is, their opposites). It is clearer in the following figure that serves as an example:

How are triangles classified?

Triangles are traditionally classified based on two criteria, which can be used together or separately. Let's see what each of them is about

  Classification of triangles according to their sides

 

Ø  A triangle is equilateral if it has three equal sides.

Ø  A triangle is isosceles, if it has two of its equal sides.

Ø  A triangle is scalene, if it has three unequal sides.

 

The following image clearly shows us one of each of these types of triangles, look carefully:

 

 

Classification of triangles, according to their angles

In this case, we look at the angles to perform the classification. Namely:

Ø  A triangle is acute, if it has all its acute angles

Ø  A triangle is a right angle, if it has one of its right angles, it is 90º.

Ø  A triangle is obtuse, if it has an obtuse angle.

Let's look at the following figure to take a good look at this classification:

 

 

Ø  How is the perimeter of a triangle calculated?

Like the perimeter of any other polygon, the perimeter of a triangle is calculated simply by adding its sides.

Ø  How is the area of a triangle calculated?

As in almost all cases, we have a mathematical formula that allows us to find the area or surface of a triangle, whatever it may be, in relation to all the categories we saw before. In all cases, the area or surface of a triangle is calculated with the following formula:

 

In the case that we see in the image, it is observed that the height is equal to 6 cm and that the base is 4 cm. Therefore, when applying the aforementioned formula, we would be multiplying these two measurements which would give us 24 cm, when dividing it by two, the final result is 12 square cm. Let us remember that in the measurements of surface, we speak of square cm, square meters etc.

 

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Fundamental properties of triangles.

The sum of internal angles of a triangle is equal to 180:

An exterior angle of traingle is equal to the sum of the interior angles no adjacent to it

EXERCISES

1. In the figure find X

    

a) -6°           b) -8°          C) -10°         d) -20°             e) -62°

We know that the sum of the interior angles of triangle is equal to 180°, so:

2. In the figure find X

                                    a) 39°         b) 52°         c) 61°         d) 121°         e) 102°

We know that the measure of an external angle is equal to the sum of the interior angles not adjacent to it, so:

 

PROPERTIES OF TRIANGULES

 

A triangle can be defined as a polygon with three sides, or as a polygon with three vertices. The triangle is the simplest polygon and the only one that does not have a diagonal. Three non-aligned points always define a triangle (both in plane and in space).

Every triangle has 3 sides, 3 vertices, and 3 interior angles. Their specific name is TRIGON, although they have been commonly called TRIANGLES, a form that has spread and is how most people know them.

The sum of the three interior angles of a triangle is always 180°

EXAMPLE

Given the following figure determine the missing interior angle, since two of its measurements are known.

Properties of the triangle

 

properties of the triangle

 

 

Presented by:

Fernando Enrique Vásquez Betancourt, Cód. 10177215

Tatiana Mosquera Mosquera, Cód., 35545485

Édison Vargas Vaquero, Cód. 6805863

Yesica Tatiana Galeano Henao, Cód. 1152207310

Rodrigo Vivas Ramírez, Cód. 96353651

 

Geometría Plana

Grupo 551106_13

 

 

Eduard Yezid Gutiérrez Barrera

Tutor

 

College Nacional Abierta y a Distancia UNAD

School of educational sciences ECEDU

 2020

Activity of: Yesica Tatiana Galeano Henao 

calculate ¨x¨ 

a)1°

b)2°

c)3°

d)4°

e)20°

solución 

as it is an isósceles right triangle, the following is given:

20x+5°= 45°     20x=40°       x=2°

answer: b)