8. Flat geometry

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Plane Geometry, also known as Euclidean Geometry, is one of the most important topics for the Enem test. It covers concepts related to two-dimensional figures such as points, lines, angles, polygons and circles. It is an area of ​​mathematics that requires a good conceptual understanding and the ability to solve practical problems. We will address some of the main topics in Plane Geometry that are often asked in Enem.

1. Points, Lines and Angles

The basic concepts in Plane Geometry are points, lines and angles. A point is a location in space, which has neither size nor shape. A line is a series of points that extends indefinitely in both directions. An angle is formed by two lines that meet at a point. Angles are measured in degrees and can be classified into several types, such as acute (less than 90 degrees), straight (90 degrees), obtuse (greater than 90 degrees), and shallow (180 degrees).

2. Polygons

A polygon is a closed figure formed by straight lines. Polygons can be classified according to the number of sides they have. For example, a triangle is a polygon with three sides, a square is a polygon with four sides, and so on. It is important to know the properties of different types of polygons, such as the sum of the interior angles and the measure of each interior angle in a regular polygon (a polygon with all sides and angles equal).

3. Circles

A circle is a plane figure composed of all points that are the same distance from a central point, called the center of the circle. The radius is the distance from the center of the circle to any point on the circumference of the circle. The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius of the circle. The area of ​​a circle can be calculated using the formula A = πr².

4. Pythagorean Theorem

The Pythagorean Theorem is one of the most useful tools in Plane Geometry. It states that in any right triangle (a triangle with an angle of 90 degrees), the square of the measure of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the measures of the other two sides. This is a formula you will use frequently to solve Plane Geometry problems on the Enem.

5. Similar Triangles

The similarity of triangles is another important concept in Plane Geometry. Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. This is useful for solving problems where you need to find unknown measures in a triangle.

6. Area and Perimeter

Area is a measure of the space within a figure, while perimeter is a measure of the distance around a figure. There are specific formulas for calculating the area and perimeter of different types of figures, such as squares, rectangles, triangles and circles. Knowing and understanding these formulas is essential to solve Plane Geometry problems in Enem.

7. Trigonometry

Trigonometry is the study of the relationships between the angles and sides of triangles. It is often used in Plane Geometry problems. The three basic trigonometric functions you need to know are sine, cosine, and tangent. They are defined for an angle in a right triangle as the ratios between the sides of the triangle.

Studying Plane Geometry for the ENEM may seem challenging, but with a solid understanding of the basic concepts and lots of practice, you can master this section of the test. Remember that problem solving is a skill that develops over time, so keep practicing and reviewing concepts to improve your skills and build your confidence for exam day.

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99. Spatial geometry