In the previous section, when you studied lines and angles, you learned that lines could be defined by just two unique points. In this section, we will learn about a polygon composed of three vertices and three sides: the triangle.
The importance of the triangle to mathematics and the world around us is absolutely tremendous. For instance, in the discipline of geometry, we will see that the triangle is the basic building block of all two-dimensional polygons, including rectangles, squares, rhombuses, and kites. Thus, we will be able to utilize some of the knowledge we gain from triangles to help up learn about different shapes.
Triangles are also of great significance in our everyday lives. The buildings around us and the bridges we ride over are guaranteed to have triangles in their construction. Moreover, the trigonometry behind triangles has advanced some of the latest developments in technology including GPS systems, satellite imagery, and cell phone frequencies. As you progress through this section, you'll develop a greater appreciation for triangles and their value.
Main Lesson: Triangle Classifications
Learn how to classify triangles by the lengths of their sides and the measures of their angles.
Angle Properties of Triangles
Main Lesson: Angle Properties of Triangles
Connect your knowledge of angles to triangles and get introduced to significant theorems including the Triangle Angle Sum Theorem and the Exterior Angle Theorem.
Main Lesson: Congruent Triangles
With the help of CPCTC and the Third Angles Theorem, learn how to prove that triangles are congruent.
Triangle Congruence - SSS and SAS
Main Lesson: Triangle Congruence - SSS and SAS
Introduction of two postulates that will help us prove congruence between triangles: the SSS Postulate (Side-Side-Side) and the SAS Postulate (Side-Angle-Side).
Triangle Congruence - ASA and AAS
Main Lesson: Triangle Congruence - ASA and AAS
Learn how to use the ASA Postulate (Angle-Side-Angle) and AAS Postulate (Angle-Angle-Side) to help us prove that triangles are congruent.
Properties of Isosceles and Equilateral Triangles
Main Lesson: Properties of Isosceles and Equilateral Triangles
Discover key characteristics of isosceles and equilateral triangles and work your way through five helpful exercises.
Right Triangle Congruence
Main Lesson: Right Triangle Congruence
We've learned about the congruence postulates of any triangles. Now, let's learn about those that apply specifically to right triangles.
Bisectors of Triangles
Main Lesson: Bisectors of Triangles
Take a look at perpendicular bisectors and angle bisectors, as well as how to use them for geometric computations.
Inequalities and Relationships Within a Triangle
Main Lesson: Inequalities and Relationships Within a Triangle
Learn about the different inequalities within a triangle, including the Triangle Inequality Theorem. Also, take a look at some helpful angle-side relationships of triangles.