Triangles

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.

Triangle Classifications

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.

Congruent Triangles

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.