Learn Geometry: Identifying Points, Lines, Planes, and Angles - Essay Sample

Paper Type:  Essay
Pages:  5
Wordcount:  1220 Words
Date:  2023-04-10

Expectations by the End of the Topic

At the end of this topic, I expect students to be in the right manner to tackle any geometric problem. They should recognize any geometric figures that are based on their experience. Students have to investigate geometric shapes at their level of identifying the properties of the figures. As a teacher, I have to ask the students to give the difference between correct and incorrect examples in geometric concepts. By doing this, the students will be able to avoid misconceptions. Asking them to make drawings on incorrect and correct examples on their own concerning the concept. For instance, asking them to be parallel and unparalleled lines, drawing quadrilaterals as well as parallelograms, and still, those who are not. In the end, the students should be expected to give the definitions under this concept. This makes the students familiarize themselves with the critical properties used in the definition. The teacher is expected to allow the students to carry out some investigations and experiments under geometric figures and ideas taught in class. They should use drawings, manipulatives, and software in their experiments. Have the students' brand short and main notes under the geometry concept filled up with appropriate examples, definitions, and non-examples.

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Warm-Up Activities

In the case of pre-requisite warm-up exercises, the students will have to do much on texts. There will be one individual assignment assessment text. The students will have to do an assessment of this geometric concept. By giving them, such will enable them to understand whether the students understood the concept well. There will also be a group work assignment as one of the assessments to the students. Students will have to form small groups to undertake set subtopics under geometry and solve the problems on their own. In this case, they will research more on the topic to cover what might be left out during the teaching process. There will be a seating, continuous assessment test (CAT) set on this concept. The CAT will cover the central part of the geometry. Then at the end of topic learning, students will have to do main examinations, which will cover the whole topic. This will make the students familiarize themselves with the geometry properties. By giving the students, all this assessment will help the teacher to analyze whether the students understood or not and will be in a position to decide whether to proceed with other topics or will take them back through the text.


Geometry is a mathematical study that focuses on the education of size, relative configuration, spatial properties, and shapes. It word that was derived from the Greek word meaning the measurement of earth. Geometry is among the ancient sciences. It was developed and organized by Greek mathematician known as Euclid back at 300 BC. Euclid in his 13 books titled Elements organized 465 prepositions of geography. Therefore, geometry has been subjected to many countless developments (Euclid's, 2020). Hence, there exist so many geography types. These include non-Euclidean, algebraic geography, simplistic geography, Riemannian geography, and Euclidean geography. The discussion primarily points out the properties of lines, angles, and points. More emphasis will be put on a geometric measure of areas, volumes of deferent shapes, and lengths. Before finalizing this class, it would be hard to conclude that geometry is surrounded us.

Euclid's Element

In-text titles' Euclid wrote a significant advancement in geometry back 300 BC. Euclid showed the form of an ideal axiomatic, which is currently referred to as Euclidean geography. In this context, he stated that propositions could be proved as accurate if they have a small set of remarks (Euclid's, 2020). From these 'Elements,' Euclid was able to formulate a considerable portion of geometric planar in five postulates. They include:

  • Two points can be joined using a straight segment line.
  • All congruent represents the right angles.
  • Any straight line segment, the radius can be used to draw a circle with one point as middle place.
  • Any two points can be joined to draw a straight line segment.
  • Two lines that are drawn to interest with a third line, the sum of the interior angle on one die is less than two right angles, and then the two lines must intersect with one another on that side if extended.

This fifth Euclid's postulate is also referred to as parallel postulates.

Rene Descartes' Coordinate Geometry

The tremendous incoming enhancement in the area of geometry occurred in the 17th century when Rene Descartes found coordinate geometry. Equations and coordinates illustrate proofs when used in this mode of geometry. The invention of parallel geometry calculations formed the basis for the development of physics and calculus.

The Invention of Non-Euclid Geometry

Janos Bolya, Nikolai Lobachevski, and Carl Friedan Gauss during the 19th century invented a non- Euclidean geometry. The first four postulates of Euclid remained consistent in this form of geometry (Euclid's, 2020). Therefore the idea that parallel lines do not meet did not remain faithful. This knowledge is accelerating the force behind hyperbolic geometry and elliptical geometry.

Proof on Two-Column Geometry

Writing ways of solving geometrical problems in the form of two-column evidence will enable us to organize thoughts efficiently. Again it will show that we have solutions for all claims that we make. It will be like time children ask why repeatedly. Their question can be annoying and may go without a solution. With the help of two-column proof in geometry, we can get all answers and conclusions on these 'whys' questions.

Main Activity for Students

This will entail measuring of lengths of different objects which enable students to comprehend various units of measurements. Collecting images that are cones or spherical will aid students to recall different geometrical shapes. Even when students grow older, they should continue to practice geometry as it will enhance their learning. For middle schools, geometric activities involve using tangrams or garboards will aid students in learning about shape properties. Students make fun of toothpick puzzles geometric operations, this enable them to put into practice their reasoning skills.

Geometric activities interactive by every nature enable students to comprehend concepts of geometry more and recall them over a long time. Geometric activities are fun; therefore, make students understand them easily without struggling. Circling shapes some dihedral angles like obtuse, acute and right angles might be confusing; hence students will be required to sort them well. This will help students to differentiate them, therefore, increasing their ability to understand (Euclid's, 2020). Cat and rat- students will be required to be ready for random assessment text all the time after completing the geometric topic. This will gauge the level or determine whether students have understood. Constructing angles by the end of each sub-topic, students will be required to build different types of aspects; for example, acute angles. They should be able to construct deferent geometric shapes.


Primarily, I expect the students to have a broad understanding of geometry and its importance to our everyday life. The students must also be able to recognize the connection between and world history. Additionally, I expect everyone student to have a great understanding of major historical figures in geometry and where it evolved. The student will know exploring scientific ages and specialization as far as mathematics subject is concerned as a whole.


Euclid's definitions. (2020). Retrieved 27 February 2020, from http://mathshistory.st-andrews.ac.uk/HistTopics/Euclid_definitions.html

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Learn Geometry: Identifying Points, Lines, Planes, and Angles - Essay Sample. (2023, Apr 10). Retrieved from https://proessays.net/essays/learn-geometry-identifying-points-lines-planes-and-angles-essay-sample

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