REVISÃO OBMEP FASE 2 - GEOMETRIA

Introduction

This tutorial is designed to help you understand key concepts of geometry as they relate to the OBMEP (Olimpíada Brasileira de Matemática das Escolas Públicas) Phase 2. Whether you're preparing for the competition or simply want to enhance your geometric skills, this guide provides actionable steps and insights.

Step 1: Understand Basic Geometric Concepts

Familiarize yourself with essential terms

• Point: A location in space with no dimensions.
• Line: A straight path that extends infinitely in both directions.
• Plane: A flat surface that extends infinitely in all directions.

Learn about different types of angles

• Acute: Less than 90 degrees.
• Right: Exactly 90 degrees.
• Obtuse: More than 90 degrees but less than 180 degrees.

Step 2: Explore Geometric Figures

Study common geometric shapes

• Triangle: A three-sided polygon; remember the types (scalene, isosceles, equilateral).
• Quadrilaterals: Four-sided figures like squares, rectangles, and trapezoids.
• Circles: Understand the properties, such as radius, diameter, and circumference.

Practice calculating the area and perimeter for each shape. Here are the formulas

• Triangle Area: ( \frac{base \times height}{2} )
• Rectangle Area: ( length \times width )
• Circle Area: ( \pi \times radius^2 )

Step 3: Apply Theorems and Properties

Learn and apply key theorems

• Pythagorean Theorem: In a right triangle, ( a^2 + b^2 = c^2 ) where c is the hypotenuse.
• Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Understand the properties of similar and congruent figures

• Similar Figures: Same shape but different sizes; corresponding angles are equal, and sides are in proportion.
• Congruent Figures: Identical in shape and size.

Step 4: Solve Geometry Problems

Practice sample problems to reinforce your understanding

• Calculate the area of various shapes given their dimensions.
• Use the Pythagorean Theorem to find missing side lengths in right triangles.

Work on problems that require applying multiple concepts

• For example, find the area of a triangle formed within a rectangle.

Step 5: Utilize Resources for Continued Learning

• Review geometry content on educational platforms or YouTube channels like Só o Mi.
• Join study groups or communities focused on OBMEP preparation for collaborative learning.
• Follow social media accounts that share math problems and solutions to stay engaged.

Conclusion

By mastering basic geometric concepts, understanding figures, applying theorems, and solving problems, you will enhance your skills and prepare effectively for the OBMEP. Continue practicing and engaging with resources to further solidify your understanding. Good luck in your studies and competitions!