Mathematics 101
- Reminder of Fundamentals
- Advanced Arithmetics
- Introduction to Geometry
- In-depth Geometry
- Deeper into Numbers
- Further into Algebra
- Elementary Statistics & Probability
- Advanced Statistics, Probability
- Mathematical Logic
- Calculus
- Calculus
- Trigonometry I
- Trigonometry II & Conclusion
Introduction to Geometry
Understanding the Concept of Angles
Something that is formed when two rays meet at a single or same point.
Angles are a fundamental concept in geometry, playing a crucial role in defining and understanding shapes and patterns. This unit will provide a comprehensive understanding of what angles are, how they are measured, and the different types of angles we encounter in geometry.
What is an Angle?
An angle is formed when two lines meet at a common point. This point is known as the vertex of the angle, and the two lines are the arms or sides of the angle. The amount of turn between these two lines is what we refer to as the 'size' of the angle.
Measuring Angles
Angles are measured in degrees (°). A full turn, or a circle, is 360°. The degree measure of an angle tells us how much one of the arms needs to be rotated around the vertex to coincide with the other arm.
Types of Angles
There are several types of angles based on their degree measurements:
- Acute Angle: An angle that measures less than 90°.
- Right Angle: An angle that measures exactly 90°. It forms a perfect L shape.
- Obtuse Angle: An angle that measures more than 90° but less than 180°.
- Straight Angle: An angle that measures exactly 180°. It forms a straight line.
- Reflex Angle: An angle that measures more than 180° but less than 360°.
- Complete Angle: An angle that measures exactly 360°. It forms a complete circle.
Angle Properties of Geometric Shapes
Different geometric shapes have different angle properties. For example, all angles in a square are right angles, while a triangle has angles that add up to 180°.
Complementary and Supplementary Angles
Two angles are said to be complementary if their measures add up to 90°. Similarly, two angles are supplementary if their measures add up to 180°. These concepts are often used in solving geometric problems.
By understanding the concept of angles, you will be able to identify and classify different types of angles, understand their properties, and apply this knowledge to solve problems in geometry. This foundational knowledge will be built upon in the subsequent units and modules.