Geometry is the study of shapes and sizes. A geometer studies the length, area and volume of various objects, and comes up with ways of understanding them better. He starts off by learning about angles and shapes, and figuring out the relationship between these ideas. This allows him to make predictions and draw conclusions about the physical world. For example, the inclination of a hill, the maximum tilt of a space shuttle before launch, and the path of a pool ball when it bounces off the side can all be expressed in terms of an angle.
Here are some tips for you to get started:
- Draw out the geometry diagram, as it helps you get familiar with it.
- Write down everything that you know, which makes it easier to chase down various angles.
- Use known relationships like the sum of angles in a triangle, and the sum of angles at a point.
- Recognize parallel or perpendicular lines, and use their properties.
- If you're stuck at one part, zoom out and look at the big picture
What can we say about the base angle of an isosceles triangle?
Draw out the geometry diagram:
We already have the image drawn out for us. The base angles are marked in green.
Write down everything that you know:
An isosceles triangle has 2 equal sides, and the corresponding base angles are equal.
Use known relationships like the sum of angles in a triangle:
If the vertex angle is , then the base angle is , which would be less than . Hence, this angle is acute.
Geometry problems involving angles and shapes can be classified as
- Basic information about angles: Picking up the terminology allows you to quickly understand what is being talked about. When in doubt, do a search for the term.
- Parallel Lines and Perpendicular Lines: Recognizing pairs of parallel and perpendicular lines allows you to exploit their properties. This is extremely useful when finding angles.
- Properties of Triangles: These comprise the basic building blocks of shapes. A strong grasp of this fundamental concept will allow you to develop much further.