Parallel Lines and Ratio Proof

Parallel lines have many important properties that you have to memorize in order to be successful in proving problems. In this post, we will discuss the properties of parallel lines intersecting two other lines. We are going to show the relationship among three parallel lines intersecting two lines. In the figure below, parallel lines l, m, […]
Continue reading…

 

Proof that sin(-θ) = – sin(θ), cos(-θ) = cos(θ), and tan(-θ) = -tan(θ)

In order to understand the proof below, you must have a prior knowledge about circular functions. The proof also uses symmetry which is I think quite basic for high schools students. The basic idea is that the point  is symmetric with the point with respect to the axis. The angles and are rotations with the positive x-axis as the initial […]
Continue reading…

 

Square of Odd Numbers Minus 1

Many numbers have interesting properties worth investigating. These properties can be used to introduce the notion of proofs. Teachers may try this out in middle school or high school students. Although the proofs might not be as elegant or as formal such as written in books, its notion and the reasoning behind it is more […]
Continue reading…