Quadrilaterals and Similarity of Triangles for General Studies

This course is the second in a series of geometry topics in mathematics for general studies. It begins by introducing you to quadrilaterals. A quadrilateral, in general, has sides of different lengths and angles of different measures. However, squares, rectangles, etc. are special types of quadrilaterals with some of their sides and angles being equal. This is the reason that the area of the quadrilateral depends on the type of quadrilateral it is. This course outlines the different types of quadrilaterals, their properties, and similarities with the aid of examples. The formal definitions of these quadrilaterals only give some information about them. Each quadrilateral has other properties that can be proved. For example, while a parallelogram is defined as a quadrilateral with two pairs of parallel sides, it can be proved that the opposite sides of a parallelogram must be congruent. You will learn about how to prove which type of quadrilateral a shape is.

Next, the course introduces you to similarities in Euclidean geometry. Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. You will learn about the characteristics of similarity, and how to determine whether two figures are similar or not. This will help you in proving geometric theorems and solve some problems with polygons and triangles. Ratio and proportion will be explained based on fractions. When a fraction is represented in the form of a:b, then it is a ratio, a and b are any two integers. The ratio and proportion are the two important concepts, and it is and it is an important foundation needed to understand various concepts in math and science. By the end of this course, you will have a clear vision of these two concepts and be able to apply that knowledge in your daily life.

Lastly, the course introduces you to Thales’s theorem, attributed to Thales, a Greek mathematician and philosopher. Thales initiated and formulated the theoretical study of geometry to make astronomy a more exact science. You will learn about Thales’s theorem and its converse. Then, the course analyzes the triangle midsegment theorem and midpoint theorem. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. There are several proportions that can be found when a perpendicular line is drawn. You will learn about these proportions and the Pythagorean theorem. Then, you will be introduced to special right-angle triangles in geometry. A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier. Knowledge of the relationships between angles and ratios allows one to quickly calculate various geometric problems without resorting to more advanced methods. If you want to improve your overall geometry skills, register for this course now and start learning more today.