College Math

Chapter 3: Geometry Overview Geometry is an essential part of mathematics, as it provides geometric reasoning to problem solving. We all deal with different geometric shapes in our daily lives, like circles, triangles, rectangles, squares, etc. For instance, you go for daily walk in a rectangular park and you need to see how many miles you walk daily, so you can find out by learning about the perimeter of that rectangle. Similarly, you want to get your window painted which looks like a semi-circle on the top of a square, and the painter asks you to pay him $2.50 per square meter of that window. So here you need to be aware about the area of triangle and semi-circle. Similarly, there are many more instances where you make use of geometrical shapes around you. The course in geometry will provide you with basic skills in lines, triangles, quadrilaterals, and circles that will hone your problem-solving in dealing with different shapes. In this chapter, you will learn about the concepts, classification, properties and theorems of triangles, different quadrilaterals and how they differ from each other, parallel and perpendicular lines in a plane and circles. Objectives By the end of the chapter, you will be able to learn the concepts and their application in: • Triangles and their types • Area and perimeter of triangles • Quadrilaterals- classification, area, and perimeter • Parallel and perpendicular lines • Circles and its properties, circumference, and area • Theorems of circles to measure different angles 3.1 Triangles Triangles can be defined as any geometric figure which has three angles and three sides. Before we move to understand the properties and application of triangles, let us understand different types of angles. Angles can be classified as acute angles (that measures less than 90 0 ), right angles (measures exactly 90 0 ), obtuse angles (measures more than 90 0 ), and straight angle (measures exactly 180 0 ). The shapes of these angles look like the ones given here:

©2018

Achieve

Page 46

of 120