# TOPICS IN GEOMETRY

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## Basic Geometry as one of the Topics in Geometry

This is the first chapter of the subject. It primarily focuses on the basic features of Euclidean geometry, which is a standard mathematical system that consists of techniques that assume the small set of subjectively appealing axioms and deduction of the other propositions.

The student learns about the definition of geometric concepts such as lines, planes, points to mention a few, and more progressively elaborates on the classification of figures like triangles, angles, and polygons. Basic geometry also focuses on the measurement of distances and angles, noting the various types of angles, the properties, and relationship respectively.

## Proof and reasoning as one of the Topics in Geometry

In this section, the student learns about the definition of the concepts and articulate their relevance to the surrounding tests. This subtopic allows the student to understand the different types of reasoning which are inductive and deductive reasoning.

It exposes the student to understand how certain things occur and where they came from based on the justification and explanations. It also aids the student in polishing their skills required to complete a two-column proof, and it provides practice in reviewing the properties of congruence and equality.

## Parallel and perpendicular lines as Topics in Geometry

The students learn about the comparison of parallel and skew lines as it presents the basic components of parallel lines. It also explores the perpendicular lines, their properties and the theorems related to them.

Another vital lesson is the different angles formed to the lines displayed and the common types of angles like alternate interior and exterior angles, corresponding angles, and so forth. You also get to earn about the relationship between the algebraic topic of the slope, distance and lines to parallel and perpendicular lines respectively.

## Triangles, congruence, types of triangles and right angle trigonometry as Topics in Geometry

In this chapter, the student gets a glimpse on triangles, the sum of angles in a triangle and the different triangle sum theorem of the external angles. It also highlights the definition of congruency with its theorems such as Third Angle Theorem. You also get to learn about the description of the perpendicular bisector, the angle bisector, and their assumptions respectively.

The student can articulate the various properties of medians and altitudes of triangles and the relationship between angles and the sides of a triangle based on the Triangle Inequality Theorem. It also simplifies the fundamental technique of the Pythagoras Theorem and its particular applications to the right angle triangle and trigonometric ratios.

This subfield elaborates on the polygon sum formula and the regular polygon interior angle formula. This provides a complete detail about the interior and exterior angles of polygons. The student also learns about the definitions and properties of squares, rectangles, quadrilaterals, trapezoids to mention a few.

## Circles

Students learn about the theorems related to tangent lines, chords, properties of arcs and central angles, and how to apply them. It also contains info about the inscribed angles, quadrilaterals and their basic features to solving problems. Last but not least, it draws the relationship between geometry and algebra as the equations of circles are reflected on the concept.

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