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Angle Measurements

Some definitions are important for angle measurements such as right, obtuse, and acute angles. In this post we are going to talk about these concepts. Adjacent supplementary angle Definition: Given a ray $\overrightarrow{oa}$ and an opposite ray $\overrightarrow{oc}$. We project a ray $\overrightarrow{ob}$ at a point in the plane. We say that the angle formed by points $b\hat{o}c$ is supplementary (supplement) and adjacent (neighbor) to the angle formed by points $a\hat{o}b$.

December 25, 2022 Read
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Angle Comparison

Angle comparisons are important for properties that will be used in later posts. Congruence Congruence in angles is a concept that is similar to equality of numbers. Here congruence is used with the symbol ($\equiv$) and this primitive notion satisfies the postulates: Reflective every angle is congruent to itself. $\widehat{ab} \equiv \widehat{ab}$ Symmetric If $\widehat{ab} \equiv \widehat{cd}$ then $\widehat{cd} \equiv \widehat{ab}$ Transitive If $\widehat{ab} \equiv \widehat{cd}$ and $\widehat{cd} \equiv \widehat{ef}$ then $\widehat{ab} \equiv \widehat{ef}$

December 15, 2022 Read
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Introduction to Angles

Angles are key parts for the development of geometry. It is present in our daily life as stairs, building cranes, constructions like the tower of Pisa, among others. In the book Elements of Euclid, this concept was well worked, even in decades before Christ. Examples of angle applications Next, we present some applications of angles. Building Crane Leaning Tower of Pisa Ladder A very used example is the clock, with movement of the hour and minute hands, the angles are formed and the time is defined.

December 3, 2022 Read
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Regions in Planes

In this post the central point of the theme is the convex region, which are fundamentals for a plane in geometry. Notions of convex region Definition (Convex Region): a set of points $\Gamma$ is convex if, and only if, any two distinct points $A$ and $B$ of these sets are one of the possibilities: endpoints of a line segment ($\overline{AB}$) contained in this set $\Gamma$ $\Gamma$ is unitary $\Gamma$ is empty

December 3, 2022 Read
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Straight lines

In this post we are going to talk about an important concept for plane geometry, which are concepts of lines, line segments, semi-lines, among others. Line segment Definition (Line segment): given two distinct points, the union of the set of these two points with the set of points that are between them, is a line segment. In symbolic terms we have the sets: $$\overline{AB} = \\{A,B\\}\cup \\{\text{for all } X \text{ between } A \text{ and } B\\}$$Consecutive segments Definition (Consecutive Segments): two line segments are consecutive if and only if one endpoint of one of them is also the endpoint of the other.

December 2, 2022 Read
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Primitive Notions

Here we start the series of posts for plane geometry. In it, we will talk from very primitive concepts, to more advanced concepts, aimed at children (elementary to medium). Start using geometry The Greeks of ancient civilization were one of the most famous people in the art of thinking. They were responsible for the heyday of philosophical, scientific, political, social and artistic ideals and had a decisive influence on the western world.

December 1, 2022 Read